Update: Ok, I just hooked the Pi up to a display, and started copying files via WiFi. After about 15 minutes the Pi just froze. I had a tmux running with output of htop and tail -f /var/log/messages. No visible kernel panic, nor anything in /var/log/messages. The machine is frozen.

Update 2: I still have problems, right now I noticed that the connection can be re-started using ifdown and ifup, but I keep getting more and more of these messages:

Mar 22 19:11:59 raspberrypi kernel: [215435.967714] cfg80211: Calling CRDA to update world regulatory domain
Mar 22 19:12:01 raspberrypi kernel: [215437.948971] wlan0: authenticate with XXXXXX
Mar 22 19:12:02 raspberrypi kernel: [215438.087245] wlan0: send auth to XXXXXX (try 1/3)
Mar 22 19:12:02 raspberrypi kernel: [215438.089006] wlan0: authenticated
Mar 22 19:12:02 raspberrypi kernel: [215438.165765] wlan0: associate with XXXXXX (try 1/3)
Mar 22 19:12:02 raspberrypi kernel: [215438.169604] wlan0: RX AssocResp from XXXXXX (capab=0x411 status=0 aid=1)
Mar 22 19:12:02 raspberrypi kernel: [215438.185759] wlan0: associated

This happens in shorter and shorter timespans until I reboot. Then it's ok again for a day or two. So what's going on here?