Parental Abandonment, by its nature, usually excludes the parent from having much of a role in a character's story. If the backstory involves a child wallowing in angst because of having no parents (maybe even hating said parents for leaving), to bring them back and treat everything as being hunky-dory sort of dilutes the origin story's dramatic impact.
Sometimes, though, a parent can be brought back through use of a proper excuse. A parent who we have seen or heard nothing of in some time may suddenly re-appear and explain that there was, in fact, a very good reason for the abandonment — but for various reasons, the details could not be revealed until just this moment. This is particularly important if child is going to follow in their parent's footsteps, since we would normally expect them to be bitter if this is the career that caused them to get abandoned in the first place.
Frequently the reason turns out to be Mom never informed Dad of their baby's existence for reasons that can range from not being sure which partner was the father (a My Two Dads scenario), or a desire to raise an infant all by herself either because she felt he would make an unsuitable father or didn't want to burden him with the responsibilities of parenthood.
This trope straddles a thin line — it can come off as extremely contrived unless said excuse is very, very convincing. In order for it to work there must be an explanation as to why no one bothered to bring it up until just the last minute.
Sounds like but has nothing to do with taunting someone about having some real or imagined flaw which leads to the parents not loving them enough. If you're looking for examples of that, try Break Them by Talking.
See also Tell Me About My Father, Daddy Didn't Show. Sometimes related to Give Him a Normal Life, and may overlap with Because You Can Cope in certain instances. If the info is specifically withheld to increase tension even though there's no good reason to withhold it, see the Rule of Drama.
Daddy Had a Good Reason for Abandoning You has been suggested to play 1 roles. Click below to see other actors suggested for each role, and vote for who you think would play the role best.