Thanks guys for the answers.
fungus:
It's certainly possible...PS: If you remove the regulator and power LED you should be able to get a sleep mode consumption of about 5uA.
yeah... unfortunately I think it too 
yesterday I searched for the datasheet of that regulator and definitely in the application note they recommend to never leave input floating... which on the other hand is weird because MiniPro allows you to use VCC pin only...
However removing the regulator and power LED was my plan too 
CrossRoads:
That sounds odd.
This remote uses 8 MHz 3.3V Promini powered with LiPo connected to VCC
When transmitting, power is ~15mA, drops down to ~5mA when in power down sleep mode in between button presses; LED uses some, Tx uses some, MAX1811 for battery charge control uses a little, maybe some leakage to the regulator. 1000mAH battery goes at least a month between charges and in frequent use.
You could try adding a diode from Vcc (anode) to RAW (cathode) to avoid reverse driving the regulator.
I know it's odd!
To be honest - yesterday I assembled another MiniPro (another clone) - this time the Mini is 5V 16MHz and uploaded exactly the same software (using exactly the same computer and Arduino IDE) and ...... The results are as you could expect!
I managed to reduce power usage to 0.2mA! (200uA) in the sleep mode - which is great! and I didn't remove power LED!
I think it could be that the other MiniPro is kind of "broken" - it works but I bought it as 5V 16MHz and it appears to be 3.3V 16MHz which is odd again 
(some midnight run?)
Obviously I re-burn the bootloader to use 8MHz internal oscillator and then even change the BOD fuse but that didn't help - MiniPro still draws 1.6mA in the sleep mode through RAW and ~30mA through VCC...
to sum up - I think this regulator is to blame.