Hi, have you built the circuit?
If all you are relying on is a computer simulation, sorry nothing like the real thing.
I presume you have a load powered by 12v derived from the mains supply, it is also charging the battery.
If the load current is not too high, just use diode switching to keep battery power applied.
Please a REAL circuit diagram please, not the simulata one. Show battery and supply and load.
Tom..... 