So turns out our NSA spyware proxy may actually be Skype.
The intermittent http losses had been getting closer and closer together and it eventually got to the point where I lost it twice in a day. I was in the middle of burning Debian CDs (to reinstall the kids laptops, because apparently using the 7.1 cds I have and upgrading is not as good as downloading the 7.2 cds and using them) and quietly simmering about having to do a clean reinstall, when Josh came up with the brilliant idea to kill Skype because apparently Skype uses port 80.
I killed Skype and coincidentally just after it shut down http was working normally again.
Josh said everything should work fine now if I fired Skype back up again.
I restarted Skype and coincidentally lost http again.