The standards for impeachment are pretty wide open and up to the House (and then the Senate), so I don't see any statutory contrary reason or restrictions to them taking up the same issues in this kind of scenario.
The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.
..... The House of Representatives shall chuse their Speaker and other Officers; and shall have the sole Power of Impeachment.
.....The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present.
Judgment in Cases of impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law.
While a President could resign and run again (more on that to follow), there's nothing magical about doing so that would prevent Congress from looking at his/her behavior, when they were President (as opposed to an argument about prior vs in-office behavior). The fact that the President took an intentional break to avoid consequences would not be a compelling argument that would make them seem more fit to hold the office.
From a more practical standpoint, I find it hard to believe that an ex-President who resigned in disgrace under a cloud to avoid formally being tossed would have any kind of viability as a candidate, either in the general election, or even in the primaries. There is the whole stink of the disgrace, but it wouldn't play well even for brain-washed cult-of-personality-followers, if that was the ex-President's base, because, if that ex-President was in the right, the resignation would signal a capitulation to the "enemy," an admission that the ex-President was not in the right, which would make the followers wrong by association, for their blind allegiance to that person. This would put a damper on the enthusiasm of that person's base of support, for sure, just from having to eat crow on social media or on comment sections of Internet news stories.
So, while theoretically possible, there's nothing to suggest it would shield that person from facing the same issues, again, and less to suggest they'd be in a position where it would matter.