When you are on shore power, the DC system runs on, typically, 14.4 volts, instead of 12.7 volts when you're on battery. If the fuses are marginal - undersized - that can cause them to fail.
You want to use the right size fuse. Smaller wires are used in automotive applications for the same fuse size than in household applications, in part because the 14 gauge=15 amps standard in household wiring is thought to be unrealistically conservative in many quarters, and in part because 12 volt
systems are more highly engineered and don't rely on plug-connected loads of unpredictable size.
One strategy to troubleshoot is to go up to 2x the fuse size and connect an ammeter and observe the circuit closely while in operation. The ammeter readings can be used to isolate the problem while the large fuse still provides short circuit protection.