... It's a model SW4024MC2. SW series.
OK. Since you say it is not giving an error then I assume you are getting no red light and the inverter is not actually shutting down, but rather it is simply disconnecting from AC power (and thus inverting), and then eventually re-syncing with the grid.
1. Is your grid power wired directly to AC1, or is it wired through a transfer switch to AC2?
2. When this happens, does the AC1 (or AC2, as the case may be) In Good indicator (green) go directly from steady-on to flashing? Or is there a short period of time where it is out altogether?
3. Please share here the values you have set for all settings under Menu 11
4. If an ATS is involved, please state make and model
With the above information I can tell you where the most probable issues are.
... I'm wondering if it would be a bad thing to set the low limit below 105.
FWIW, I keep my lower limit set at 98 volts.
The Inverter doesn't care -- it will tolerate anything down to the lowest setting it will allow. What cares are your appliances. Remember that whatever the incoming voltage is, that's what the output voltage will be. Motors in appliances like air conditioners don't like low voltage and will have a shorter lifespan.
I'd rather have air conditioning even when I am on crappy park power like in Mexico, and if I end up replacing a unit early because of it, so be it. For people who have heartburn about this, though, the solution is to let the inverter just invert (IOTW, do not pass shore power to it at all), and use a separate battery charger to provide power to the batteries and thus the inverter. Then the inverter will be putting out ~120VAC, and only the battery charger will see the crappy input power.