Lots of good advice above. Lots of possible issues. There may also be multiple issues combining to cause the shut down.
The whole system is tried and true being tested over the years. However, note that your battery bank is marginal for operating a 1000 watt inverter. The inverter will draw 85 to 95 amps when outputing 1000 watts. It may draw more for short periods while starting the refrigerator.
I recommend you check the maximum output rating for the batteries. Note that battery terminal voltage will drop a lot when maximum current is being drawn. If battery is below 100% SoC the result will be even lower. Inverter will shut down if actual momentary voltage drops below minimum programed voltage (see manual).
I have a pair of 100 amp hour AGM batteries powering my 1000 watt inverter. I test it at about 75% capacity when batteries were fully charge. Voltage dropped dramatically.
Flooded cell batteries typically support lower output than AGM. Are your 70 amp hour batteries flooded cell?
All this happens for brief periods. You may not catch it happening unless you have a maximum/minimum recording voltmeter.
Other things that may cause lower input to inverter:
- Minimum wire size used by manufacturer.
- Loose or corroded connectors on that minimum cable. Remember both positive and negative (possibly ground wire) will cause voltage drop.
- Switches, fuses, or circuit breakers in the 12 volt line from battery to inverter. They corrode and erode with time. The transfer switch associated with the inverter is one of these fixtures to be concerned about.
Of course refrigerator compressors don't become more efficient as they accumulate hours. And inverters rarely become more efficient with age. You may be pushing equipment limits and like me, the equipment may be getting less efficient.
- Remove, clean, and reinstall connectors. Discolored insulation is highly suspect.
- Increase the size of your battery bank.
- If the cable from the battery to transfer switch is long, consider pulling a larger cable.
- Inspect contacts inside transfer switch if possible. (some are sealed)