Games : GameBoy Advance SP won't load anymore

I recently got me two of my favourite games again on GameBoy Advance SP.

I played just a few hours with one device and then went to bed. On the next day, the battery was empty - ok. But trying to charge it again failed.

When I plug in the power source to my GBASP, the "loading LED" lights orange (intended) for only 1-2 seconds and then turns off (not intended). The loading process is then aborted.

Luckily I got another GBASP for me, which loads with the same power source perfectly, but I want to know if I can easily repair this damage.

Is this a known problem and how can I repair it?