Sorry for the late update.
This is the result of badblocks:
root@Nas:~# badblocks -b 4096 -s -n -v /dev/disk1_6
Checking for bad blocks in non-destructive read-write mode
From block 0 to 240437500
Checking for bad blocks (non-destructive read-write test)
Testing with random pattern: done
Pass completed, 0 bad blocks found.
So, it found no issues (at least in non-destructive read-write mode)...
I tried memtester with at least the available free RAM. No issues here too.
Today I could reproduce the case quite fast.
This is a sequence of 'ps2 aux' outputs during the bad sceneario:ps_log.txt
This is a sequence of 'htop' outputs (generated after the ps outputs):htop_log.txt
As mentioned before, the system is successively getting slower and slower within some minutes and finally not resonding at all. I hope that someone has a hint for me (am still hoping that it's not the disk).