Remotes will work only 5 minutes after lock

[roskoant]

Hello, guys!
Car is BMW E60 year 2004.
I have a strange problem and after significant reading, I can't seem to find anything that is close to mine.
The car will lock as it should, it'll as well unlock, but if no more than 5 minutes has passed since the last lock (no matter from the remotes or door lock).
The CAS seems to go into sleep mode and will not receive any commands from the remotes(I have 2, they both lock and unlock).
If the car is unlocked, no matter what time has passed since last unlock, it'll lock.
Now the interesting part - if I go and put the key in the door lock and turn it into lock position (unlock also works), the remotes start to operate as they should and I can unlock the car from them.
Something is happening with the power supply line that is responsible for terminal 30 in sleep mode (don't know how BMW calls this).
All fuses are good, no other electrical problems in the car!
Can it be the diversity antenna not being powered up in sleep mode?