This is an issue which has made it incredibly frustrating to do hunts with since they were first introduced. It was frustrating to both myself and the people I partied with when me crashing caused them to not receive full credit due to me not being there. I disliked being a liability so I stopped hunting a short time after hunts were first introduced.
This issue was never resolved back then so I'm going to try again.
Specs:


I have the latest catalyst driver.

Due to how busy hunting is right now and how you can come across hundreds of people in one small spot, it causes the ffxiv.exe process to go above 1.3GB in memory usage. When it gets that high I experience extreme slowdowns which almost always lead to a crash like the one pictured here:

It was speculated that it was an issue with the series of GPUs that mine is a part of yet there was no actual fix given.
I have yet to try hunting on the lowest possible graphic settings so I will be giving that a go today and will report on whether I still get a crash.