Just an update: I have not had much time lately, but the drop outs forced me to check again - while reading the logs from both the DHCP server and from RT-N56U I was able to spot the moment WLAN stops working.
rsyslogd[356]: May 30 16:09:12 wifi kernel: [76050.920666] ieee80211 phy0: rt2x00queue_write_tx_frame: Error - Dropping frame due to full tx queue 2
My issue is the same as described here: WiFi connection dropped - Dropping frame due to full tx queue
I will try to recompile the kernel and see if it helps.