I am curious to know if states have a specific timeline for voting to ratify a Constitutional amendment and if there are any that have been passed by congress but not enough states have voted to allow ratification?
There is no time limit but it can be included in the amendment itself.
It has been accepted that Congress may, in proposing an amendment, set a reasonable time limit for its ratification. Beginning with the Eighteenth Amendment, save for the Nineteenth, Congress has included language in all proposals stating that the amendment should be inoperative unless ratified within seven years
The 27th amendment took 202 years, 223 days to get approved which shows that there isn't a time limit unless set up as part of the process. It should be noted that it was proposed at the same time as the first 10.
The anti-title amendment is still outstanding, since 1810 when the 11th Congress passed it:
"If any citizen of the United States shall accept, claim, receive or retain any title of nobility or honour, or shall, without the consent of Congress, accept and retain any present, pension, office or emolument of any kind whatever, from any emperor, king, prince or foreign power, such person shall cease to be a citizen of the United States, and shall be incapable of holding any office of trust or profit under them, or either of them."
The states have yet to ratify it - only 12 have approved the measure, compared to the 38 needed.
The same is true for the Child Labor Amendment, with 28 state signatures, which has stalled since 1937:
Section 1. The Congress shall have power to limit, regulate, and prohibit the labor of persons under eighteen years of age.
Section 2. The power of the several States is unimpaired by this article except that the operation of State laws shall be suspended to the extent necessary to give effect to legislation enacted by the Congress.
The DC Voting Rights Amendment was active 1978-1985, until it expired per the stipulations therein:
Section 1. For purposes of representation in the Congress, election of the President and Vice President, and article V of this Constitution, the District constituting the seat of government of the United States shall be treated as though it were a State.
Section 2. The exercise of the rights and powers conferred under this article shall be by the people of the District constituting the seat of government, and as shall be provided by the Congress.
Section 3. The twenty-third article of amendment to the Constitution of the United States is hereby repealed.
Section 4. This article shall be inoperative, unless it shall have been ratified as an amendment to the Constitution by the legislatures of three-fourths of the several States within seven years from the date of its submission.
Finally, there's the ERA which is most recent.
(answer focussing on the "in Limbo" aspect)
The equal rights Amendment states
"Section 1. Equality of rights under the law shall not be denied or abridged by the United States or by any State on account of sex.
Sections 2 and 3 grant the usual right to allow Congress to enforce this by law.
It was first drafted in 1923, and passed Congress in 1972.
Its status is rather unclear. Unlike other amendments, there is nothing in the amendment text that provides a time limit. However, the Joint resolution that proposed it did place a 7-year time limit on ratification. It is somewhat unclear if this time limit is valid
Moreover, several states have ratified this amendment and then rescinded the ratification, or (in one case) the rescinding has been vetoed by the governor. It is unclear if ratification can be rescinded, or if the Governor can have any role to play in this process. Other ratifications referred to the 7 year time-limit, so may have been withdrawn in 1979.
So even though enough states have at some point ratified the amendment, there aren't sufficient unambiguous ratifications, and unless Congress decides to recognise the ratification, there is no route for courts to rule on the matter.
While there is no time limit specified in the Constitution, courts have been reluctant to refer to the 27 amendment in deciding cases, which suggests that practically, very old amendments carry less influence over court decisions.
There is also the Congressional Apportionment Amendment outstanding since September 25, 1789:
After the first enumeration required by the first article of the Constitution, there shall be one Representative for every thirty thousand, until the number shall amount to one hundred, after which the proportion shall be so regulated by Congress, that there shall be not less than one hundred Representatives, nor less than one Representative for every forty thousand persons, until the number of Representatives shall amount to two hundred, after which the proportion shall be so regulated by Congress, that there shall not be less than two hundred Representatives, nor more than one Representative for every fifty thousand persons.
If this were to be adopted now the House of Representatives would have over 6000 members.
If the joint resolution passed by Congress does not have an explicit time limit, then Congress itself decides, upon notification that three-fourths of the state legislatures have ratified the amendment, whether or not the ratification is timely and the amendment becomes part of the constitution. This was one of the holdings in Coleman v. Miller. Quoting from the decision:
The Congress, in controlling the promulgation of the adoption of a constitutional amendment, has the final determination of the question whether, by lapse of time, its proposal of the amendment had lost its vitality before being adopted by the requisite number of legislatures.
... No limitation of time for ratification is provided in the instant case, either in the proposed amendment or in the resolution of submission. But petitioners contend that, in the absence of a limitation by the Congress, the Court can and should decide what is a reasonable period within which ratification may be had. We are unable to agree with that contention.
... the decision in Dillon v. Gloss, supra, that the Congress had the power to fix a reasonable time for ratification. But it does not follow that, whenever Congress has not exercised that power, the Court should take upon itself the responsibility of deciding what constitutes a reasonable time and determine accordingly the validity of ratifications. ...
... In short, the question of a reasonable time in many cases would involve, as in this case it does involve, an appraisal of a great variety of relevant conditions, political, social, and economic, which can hardly be said to be within the appropriate range of evidence receivable in a court of justice and as to which it would be an extravagant extension of judicial authority to assert judicial notice as the basis of deciding a controversy with respect to the validity of an amendment actually ratified. On the other hand, these conditions are appropriate for the consideration of the political departments of the Government. The questions they involve are essentially political, and not justiciable. They can be decided by the Congress with the full knowledge and appreciation ascribed to the national legislature of the political, social, and economic conditions which have prevailed during the period since the submission of the amendment.
Our decision that the Congress has the power under Article V to fix a reasonable limit of time for ratification in proposing an amendment proceeds upon the assumption that the question -- what is a reasonable time -- lies within the congressional province. If it be deemed that such a question is an open one when the limit has not been fixed in advance, we think that it should also be regarded as an open one for the consideration of the Congress when, in the presence of certified ratifications by three-fourths of the States, the time arrives for the promulgation of the adoption of the amendment. The decision by the Congress, in its control of the action of the Secretary of State, of the question whether the amendment had been adopted within a reasonable time would not be subject to review by the courts.
There are no pending amendments that have an explicit time limit, since said time limits have all expired. In the case of the pending amendments that do not have an explicit time limit, as mentioned in some of the other answers to this question, it is not possible to predict what would happen if a sufficient number of states were to ratify them. Congress may or may not recognize the ratification.