Not stamina per se, ruling out chaffing and it sounds like your backside is used to the saddle, my guess and it is a guess, is that you are a bit tight around the hip flexors, when you do a longer ride, they can take a bit of a hammering (along with everyting else) if they are tight already it wouldn't take much to ping em a bit.
I am not a doctor, physio or anything like that, its just that I was a bit tight around the hip flexors myself (mine was because of a prolapsed disc unknown at the time and that led to everything tightening up) and experienced a bit of pain similar to what you are describing (to be crude to pinpoint the pain the hurt felt like it was coming from deep inside my sack but underneath a bit) although in my case it was more post ride than on the ride. Once the disc problem went away I still had to work on hip flexibility a bit of stretching and Pilates or other core work largely alleviated the problem.
In my case I had that pain and sciatica as well.
As always if the problem persists and it worries you I would get along to the docs.