Inverter shuts off under load but battery shows plenty of charge

Classic symptom that points at a few specific causes, not a dead inverter:

1. Voltage sag under load — a battery can show 12.6V resting and still sag to 10.5V the instant a heavy load (microwave, coffee maker, hair dryer) hits it, especially with an undersized or aging bank. Most inverters have a low-voltage cutoff around 10-10.5V for exactly this reason.
2. Undersized or long DC cable run between battery and inverter — voltage drop under load can trip the same cutoff even with a healthy battery.
3. Loose battery terminal or busbar connection — intermittent under load, fine at rest, is the classic signature of a loose/corroded connection heating up and dropping voltage right when you need it.
4. Actual overload — check the load's starting wattage, not just running wattage. Compressor-based loads (fridge, AC, microwave) can spike 2-3x their rated wattage for a second on startup.

What's pulling the load when it cuts out, and what's your battery bank/inverter size?