Thomas, check if you pay too much.
My sites are hosted by powweb.com:
- 20 GB storage.
- 400 GB traffic/month (~13GB/day) !
- PHP / 5 mySQL databases.
- Your sites run through 5 Unix (backup) servers.
- $200 / 2 years.
http://powweb.com/PowWeb/OnePlan/Detail
I never had access problems.