is it possible to receive data from bluetooth when arduino is sleep mode?

I made a code for receiving data from hm-10 when I press button.

but the problem is that power consumtion is too much so, with 1200mA battery, only last 3~4 days.

I heard that there are plenty of sleep library that i can use for arduinno pro mini.

but is it possible for arduino pro mini to receive data when arduino pro mini is in sleep mode?

No, when the arduino is put to sleep, the processing of code is halted. The arduino either needs to be woken up by a watchdog (a timeout) or an interrupt (hardware event) to resume processing code. I'm pretty sure that somehow the bluetooth tranciever should be able to generate an interrupt, so that the arduino only wakes up to process bluetooth request and when done can be put to sleep again. But this would require the bluetooth tranciever not to be put to sleep / powered down.

But this would require the bluetooth tranciever not to be put to sleep / powered down.

Putting the Arduino to sleep, then, to save power, would be like turning off the dash lights while the starter motor is running.

kotran:
but is it possible for arduino pro mini to receive data when arduino pro mini is in sleep mode?

No its not.

What you could arrange is to put the Pro Mini to sleep and leave the Bluetooth receiver powered so that when it receives some data it wakes up the Pro Mini.

And no, the Bluetooth receiver cannot receive data when its powered down .......