Little DC Power Supply As Charger: Why Not?
These batteries have a maximum charge current of 1.35 A and your power supply has a maximum rating of 0.33 A.  Basically you are running the power supply at it's rated maximum for long periods of time.  The fact that it eventually dies is probably because it overheats.

Maximum ratings, can mean, it "can run at this current for ever", or it can mean, "will run for short periods of time at that current but don't do so for longer periods".

I think you've proven the later.