Just to make sure we are on the right track, is it your wireless network that disappears, or do you still see the network and you simply can't get any response from the internet?
If your network disappears, it is probably not the internet connection. Unless your internet company is responsible for your router, don't waste your time to bug them with this (unless we find something to indicate otherwise). Your network is independent of the internet, and should always be active, even if you disconnect your wireless router from the internet completely.
Along with the cordless phone possibility, what electrical equipment is near your computer or your wireless router? Between them? Does your network disappear every time someone uses the microwave?
Along with the phone, anything else in the house that is wireless may be an issue, such as wireless speaker systems.
It sounds like you have several other wireless networks around, I wonder if there is a potential that you and someone else are hammering each other...
Changing the frequency may address several potential issues with radio frequencies butting heads.
