A relationship that begins around Christmas and New Year (often started with a drunken hookup at a party) and that dies around Easter. A Jesus Relationship is often between two people who are incompatible, and survives for a few months due to the heightened joy around the holiday season, but dies as the year progresses.
Dan: Me and Mary weren't compatible, we were doomed to a Jesus Relationship.
Fin: Was she super religious or something?
Dan: No, it was just destined to die within a few months.