The reason was rather obvious. It had to do something with my server. I use Strato, a professional company so I didn't suspect them at first, but a google for 503 strato led to the solution. It is a security feature at Strato which can be turned off, but is on by default. I really wonder, why it didn't fire earlier, but this is how you can turn it off.
- log into your account
- choose your package
- go to Security (Sicherheit) in the menu
- choose ServerSide Security
- turn off Filter agains guestbook spam (Filter gegen Gästebuch Spam)
I hope this saves some of you the trouble of going through your scripts. Try this first if you have 503 errors.