Two 12V batteries in series for 24V power, 108 watts load for 2 hours 44 minutes, the inverter is set to turn off at 50% SoC.
2.75 h x 108W = 295 Wh
Since the inverter was set to cutoff at 50%, the batteries should have 295 Wh / 50% = ~600 Wh.
To know if the batteries are good we'd need to know the number of amp hours the battery was rated for.
600 Wh / 24V = 25 Ah.
My first guess would be improper voltage settings on the Aims charger settings. Let them sit off float for 15 min and see if the voltage of each is 13V.
What's the voltage of each battery after the test concludes (take the voltage while failing and then again 15 min afterwards)? At 50% it should be about 12V:
If the voltages are not same then one may have a dead cell. You can probably get them tested for free at a local autoparts store. Worth it if they're still under warranty.
Batteries are also rated at the 20 hour rate, that is you won't see the 105 Ah out of them unless they are discharged slowly over 20 hours (this is known as
Peukert's law). Discharging them faster means less total power. 105 Ah / 20 hours = 5.25 amps, at 24V that's 126W, so your two-light bulb test should be fine.
Here's an example chart, but check the datasheets on your batteries if you can find them:
View attachment 55819
Finally, lead acid batteries have less power availabe when they're cold. See the
Battery FAQ, for more on batteries...
Hope that helps!