I seem to have narrowed down the issue. I have the same setup as pictured above. I performed factory reset and it was solid for 20 minutes so I then slowing started configuring it one setting at a time. As soon as I enable PineAP - Beacon Response, the pineapple will not go longer than 5-6 minutes before rebooting, sometimes as little as 2 minutes. If I manage to disable Beacon response the pineapple goes back to functioning like it should.
P.S. when powered by the A/C adapter provided with my tactical kit the pineapple does not suffer these same reboots like it does when running off the two batteries.