Just a couple things -
Uprating the fuse from a 30 to a 50 isn't solving the problem - if anything it could cause more issues down the road.
Fuses can blow for many reasons, but the one underlying reason is more current than the circuit is designed to handle. Something is loading down the circuit and causing the fuse to go.
A lot of people will immediately jump to a "short", but if that were the case your motor wouldn't start/stop/start/stop before the fuse went. If it was a short the fuse would blow immediately the moment you put it back into the circuit.
The fact your motor is start/stop/starting would point me in the direction of the motor itself - the battery is getting hot because it's trying to dump current into the motor to make it go.
Without knowing what happened and going off what you've said so far, I'm betting that:
1) The motor has reduced resistance (less resistance, more current to drive it = fuse poof!) in it from when the motor was stalled, damaging the coils and reducing the motor's internal resistance
2) The motor has a thermal sensor in it and see it getting hot, so it stops it to prevent it from damaging itself.
3) Motor turns back on, current is too high
4) Fuse blows.
OR -
You've got a bad battery - the motor stalled in the mud, draining the battery and it wasn't charged up immediately afterward/it was an old wetcell battery and was starting to get tired. Even after charging you've got a float charge of 12V, but the actual capacity is much less so you when you apply the load (motor) it starves the battery of voltage (low voltage = high current) and the motor sees this causing the motor to start/stop as the voltage drops too low (eg, 11v runs, 9v's stops causing the battery to recover to 11v, and the motor runs again), and eventually there's not enough voltage to run it which spikes the current and the fuse blows.
The first option is a bit of an issue to troubleshoot, but the second option is as easy as pulling the battery down to Autozone or where ever and having them load test the battery for free.
Just a couple idea's for you.
C