I forgot to mention, I have tried to associate with
aireplay-ng mon0 -1 120 -a <XX:XX:XX:XX:XX> -e <AP_NAME>
and after that run
reaver -i monX -b XX:XX:XX:XX:XX -c X -vv

but that also results with nothing - Reaver is just stucked at "Associated with XX:XX:XX:XX:XX" forever.