I would say yes a statute of repose does exist (with one very large caveat).
Chapter 1 Section 52 limits to three years an action "For criminal conversation, or for any other injury to the person or rights of another, not arising on contract and not hereafter enumerated."
The caveat being that I found nothing in the statutes or in appellate case law that indicates that it can’t be taken to mean from the time the affair was found out as opposed to when the affair occurred (though how can your affection for your spouse be alienated fifteen years after the divorce?). It seems to me that a appellate judicial determination (or legislative determination) is in order, as a case-by-case judicial determination (which seems to be how it is done now) would seem ripe for examination as to its federal constitutionality on a Due Process claim.
Interestingly enough, I did find a case that struck me as odd. In what breads even more disturbing possibilities, in Eluhu v. Rosenhaus the NC Supreme Court upheld a Court of Appeals ruling, which held that the defendant is beyond the jurisdictional reach of NC when he’s not a resident of NC… Moral of the story: If you want to sleep with someone’s spouse make sure you don’t live in NC when you do. Which, since I live in Charlotte, could make for a very interesting case if it involved a person who lived in Rock Hill, SC having an affair with someone who lives in Charlotte, NC.
Also interesting…Alienation of affection is not set in statutory law but in tort set down in the case Henson v. Thomas (1949), which seems to hold that spouses are property.
As regards the reasonableness issue, I would maintain that the final divorce marks the boundary at which it is reasonable for a person to know of the infidelity. So much is settled by the divorce decree it is reasonable that the clock should start on this claim as well. Though I see another problem. What if you flip the time frame…
John and Jane get married. Shortly thereafter John has an affair with Joan. The affair lasts 3 months. Fifteen years LATER John and Jane get divorced for reasons wholly unrelated (at least directly) to John’s affair with Joan. During discovery Jane learns of the affair fifteen years earlier. Would Joan be subject to an AoA claim?