The 100 amp fuse/circuit breaker for the inverter may not be enough. I also have a 1,000 watt inverter. According to my manual and the calculations for wire length, I needed a 150 amp circuit breaker. Otherwise, I agree with what Steve_S suggested. The only true fuse in my system is downstream of the battery and it's a 225 amp Class T fuse.
Do you have a shore power connection? Is your inverter connected to the main AC distribution panel in the RV?