So some observations as I troubleshoot...
First, the mosfet chosen for the guns, the FQP33N10, has a Rds(on)Vgs of 10v which makes it a poor choice for this application.
The drive circuit is a microcontroller that can only supply 5v to turn on the fet, so the fet is never "fully ON". In fact it takes 10v to turn on the FET fully. This makes it generate way more heat via internal resistance every recoil fire.
This, coupled with no heatsink on the fet leads to premature failure of the part - least that's my thought.
Ok with that out of the way, there is also no pulldown resistor on the gate. This kind of leaves the gate "floating" - and since it's floating the device seems to be fairly unstable. I added a 1k resistor between gate and ground and the device would stay off until triggered.
https://electronics.stackexchange.com/questions/45494/what-happens-when-a-mosfets-gate-is-left-openI'm going to dig into and test further. It may be as simple as adding a pulldown resistor to keep the fet from coming on, though this does not solve the issue of only partially turning on the FET with a Vgs of 5v.
So for me, I'm going to replace the FET with one that is meant to be triggered by logic levels. I've chosen the IRLZ44N which has a Rds(on) Vgs of 5v. The IRLZ44N has a lower max voltage of 55v but that's well over the 36v of the recoil, plus it has extremely low internal resistance when fully on (cooler running). Another suitable part would be the IRL540N which is more similar to the FQP33N10, but with an appropriate Rds(on) voltage of 5v.
I'll let you all know how I do.