In a recent game, shortly before the end, we were in this position:
At this point, my opponent played on h5 to protect against an invasion at g5. But I could not see a way to make that invasion work and still cannot see it. Can someone weigh in and tell me if there was an opportunity to do anything other than miserably die inside the black stones?
I couldn’t find anything there.
if a1 gets filled, and no black defensive stone in h5 area, i get it to that white h6 => seki (or black has to sacrifice something)
edit: actually even without a1 getting filled, white h6, if black respond h5 i get it to seki anyway…
edit again: g5 stopps it, so no… not seing anything anymore, unless g5 itself might work as an attack…
No. Nothing. can’t see anything…
Seems to be like your opponent may have done what opponents do sometimes, and made a mistake 
The cuts don’t work directly, and f5 and g5 can be considered miai (except there are other options sometimes as well to defend… And there are some nice traps there, but nothing seems to work to me)
Odds are that he just lost a point.