so much more info needed, but batteries running low is a good start, wiring being too small from the battery to the inverter is next (if it's a new system).
do you have a volt meter that you can measure things with?
If so measure across the input terminals of the inverter and also at the batteries themselves when it's shutting down. If you see a big difference between the two locations it's the wires, and if you're seeing much less than 11.8v (for a 12v system) at the batteries themselves you're likely just killing your batteries.
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