On my circuit, with the MSP430f6638 micro controller and some other chips (most of which I have removed)
I have the device running in low power mode and drawing about 15 microamps. If I disconnect power and let the voltage drop (capacitor discharge) to right about 0.9 V, and then turn power back on, the device will draw about 3 milliamps when it is low power mode. If I reconnect power when the voltage is greater than about a volt or less than 0.7V, it always is in the normal 15 microamp mode for standby.
It won’t exit the 3 milliamps standby “mode” unless I unplug power and let the voltage drop below about 0.7 V before turning back on.
Restarting the micro without letting power discharge always doesn’t resolve the situation.