Sure, just call SBC and ask them for a list of compatible modems. Find out if the list is available on their website somewhere, or see if they can e-mail the list to you so you have it in writing. If you buy something and it doesn't work, then you have documentation of SBC saying it should work. If the router isn't that old, you could call up 2Wire and ask them if they can replace it.
I have delt with SBC DSL before, bunch of pricks. Check to make sure the DSL line is not droping off. (light on modem orange) I had a friend that had a connection problem. It was due to a DSL line not running a high enough signal for the connections to be stable.
Also 2Wire has not impressed me. He had 3 go bad in less than 6 weeks. So far in a 9 mo period he's on his 4 or 5 unit.
Also check your lan settings. There is a lease time that may be expiring. It will only apply to the lan side. The WAN side is controlled by SBC.
Depending on the time. SBC may be doing maintance. But it sounds like a lease time is expiring.
It could be that it always happens at the same time because the "lease" time is 24 hours, so it always expires at the same time of the day. One thing you might try is seeing if you can use the 2wire in bridge mode. This would essentially make it act as a DSL to Ethernet converter, so the actual login, etc would happen on your PC. Only downside to that is you would probably want to get another Linksys-type DSL router because bridge mode would only support one PC.