The thread seems to be about how if you miss your chance one time, the trainer will show up later in the story to give you another chance. What I want to know is do you ever run out of chances?
After hopping around bulbapedia for a while, I believe the following Pokemon can be safely 100% refought at any time in the post game:
Owned by regular trainers, like Pyrite's battle square and Pyrite cave.
All of the Cipher Peons with Shadows in the Cipher/Shadow Pokemon Lab can reappear in the Post game until you've captured them
Other Cipher Peons (the ones you fight in Realgem) & Skrub (the guy with Hitmontop) will instead show up at the Snagem hideout until you've captured them
The Johto starter peons I think don't permanently disappear until you capture their shadows
The 4 randos, Nascour and Evice in Realgem
Agnol, since I believe you can always do the final round in the Deep Colosseum.
Fein does
not leave until you capture Togetic if this note on bulbapedia is accurate.
At first I thought you could miss out on Gonzap's Skarmory, but rereading it while doing a second pass for accuracy I saw that he will stick around
until you've captured the Skarmory at which point win or lose he leaves.
You're forced to capture Makuhita so he doesn't matter
I couldn't be sure if the Smeargle & Ursaring trainer in Snagem stick around or not. Considering the rest of Snagem does stick around, I assume they do? But not 100%
Bulbapedia was unlcear if the Admin's rounds of Deep Colosseum can be replayed, so it's possible those ones are limited
So....it seems like it's literally everyone except maybe the Admins?