Does the Senate have the ability to block a subpoena submitted by the house of representatives?
No. A congressional subpoena is issued by the House of Representatives or the Senate on its own authority (for example, a recent subpoena (pdf)):
By Authority of the House of Representatives of the Congress of the United States of America
The subpoena could be challenged in court by someone with standing to do so. This would normally be the person to whom the subpoena is addressed. Neither the senate nor any senator would be likely to have standing.