If I'm sustaining Enhance Ability on myself by concentration, and then during a combat that arises a few minutes later, I try to cast Hold Person on an enemy, but they pass their first roll to save against the effect so the spell essentially did nothing (and didn't need to be concentrated on/sustained), does that still end the original spell I was concentrating on (which I was planning to give up on but now might as well continue)?
You will still break concentration if they make their save. From page 80 of the Player's Basic Rules, the section on Concentration:
Casting another spell that requires concentration. You lose concentration on a spell if you cast another spell that requires concentration. You can’t concentrate on two spells at once.
You lose concentration when you cast another spell that requires it. It doesn't matter whether that spell does anything, as long as you cast it. If you had somehow been prevented from casting Hold Person at all, you would not break your concentration, but you cast the spell, and the fact that it didn't achieve anything is immaterial.