Lastly it appears your battery is dual purpose battery(not a true deep cycle). Any battery with CCA or MCA is not a true deep cycle battery.
Dual purpose batteries should not be discharged more than 20% (maybe 30%) or you risk damaging them. A true deep cycle battery can be discharged to 50%...
You won't be able to run an AC overnight with a $1000 battery bank. When the sunsets/night, what really matters is the amount of energy/stored in your battery bank. A small 5000BTU window AC uses around 500w every hour. Battery technology is not ready for heavy demanding power hungry appliances...
I just had the same problem with a different model - Allpowers R600 beige. It arrived dead on delivery and wouldn't charge via solar/dc charging. However it would charge via AC charging.
Did your unit arrive with dead battery (0%)?
Never leave FLA batteries in a discharged state. If you won't be using them, have them connected to a float/trickle charger to keep them topped up. If you let them sit in a discharged state for more than 24 hours, you may state noticing drop in capacity due to sulfation.
Always check the water...
The 20 hour rating for your battery bank should be 2*100Ah/20h = 10A. Anything over 10A reduces your capacity because of Peukeurt Law. I am assuming your 300watt appliance is drawing around 25A / 0.8 * 0.9 = 35A from your battery bank using an inverter. 80% efficiency due to battery discharge...
I agree. The battery bank needs to be fully recharged the next day. 100 watts is not enough to fully recharge your battery bank. The battery may be sulfated and lost capacity. You need at least 300-400 watts if you get 5 hours sunlight to fully recharge your battery bank from 50% to 100 %. Just...