I tamed a female Mermaid Cove Qitari in the Summer Exploration Zone (Esior's Cove) about 20 minutes ago, and it both took the standard trap that I used and gave me a success screen, but was not present in my stables when I went to check for it later. It only had traits present in M3 (BD).

I found this highly irregular as I caught another themed luffox just a few minutes before and that one was in my stables, but the Qitari wasn't.

are you sure it was a success? Technically there isn't a 'success screen', there's just a note in the battle log that says the pet was caught and provides a link to the pet.
A battle ending isn't a 'success screen', since there's several outcomes for trying to catch a pet in non-lost grove areas:
> Sylesti is not caught, battle continues
> Sylesti caught, battle ends (if sylesti was only enemy on the field, as is the case for all fest zone themes), link to pet provided in battle log
> Sylesti not caught, sylesti flees the battle, battle ends (again, if it was the only enemy on field)

I expect what happened was the qit just escaped the trap and fled the battle?

I thought the screen said that I'd caught the sylesti, but maybe I just exited too fast and misread the text. I suppose I might have since I'm not wearing my glasses at the moment. Sorry for the trouble, I was just a little confused and worried since I had been trying to catch it for someone else.

This almost certainly means that the pet ran away instead of being caught. You can always verify the result of a trap by reading the battle log after the trap is used. If the pet was caught, it will provide a link to the new pet's profile page and that way you can verify it was successful.