Unfortunately, I do not have much experience with AT-slave firmware and do not have any device around to test. According to specs any activity on RX pin should wake up the module. Which makes sense to me.
Seems like you have an issue with power supply. Check your wiring and supply voltage - it has to be in the range from 2V to 3.6V. Also if it is too noisy or cannot handle sudden current changes without significant voltage changes, then MC can go into random state and ‘freeze’. If voltage is ok - may be add a decoupling capacitor? 1uF or higher - the higher the better
0.5mA is what I would expect with UART staying always on, but they seem to switch UART off in deepsleep. This is what I make from reading their specs. Do you have a scope? To look at the power line and RX pin - how much noise is there.