I had the same problem a few days ago

I called ATT tech support, and they instructed me to reboot everything in order (DSL modem, then router, at last computer). It only worked for an hour or so, then the router lost the connection again. I have to turn the power of the modem off, and back on again to get a new connection. But it would only last about 20 minutes.

I was using the old DSL modem from 4 years ago, and I also had a new one (much smaller) SBC sent me last year. I decided to replace the modem this time (next would be the router). And bingo! The problem never happened again.

Maybe you can try it yourself. If you need a new modem, you can buy one from Ebay for about $15. Or if your contract is up, you can get a new one for free after rebate by discontinuing your service and signing up as a new customer. But the cost of shipping is about $15.