Hi
There is always the possibility that hardware goes bad.
Your 2Wire is actually a Modem Router.
Log to the Router look at WAN side and make sure that it configured to keep the connection alive.
If this device was given to you by the ISP call their support, they will help with this.
Otherwise, you have to establish whether you lose the connection from the computer to the Router, or the Router loses its connection to the Internet.
When you do lose the connection try to connect to the Routers menus (read the manual) if you can connect to them than it is Internet connection problem.
Here you have some "stuff" about this Modem/Router.
This is for an ATT connection YMMV.
http://www.server-servers.com/att-dsl-2wire-2700hg-b-router-setup/
Jack-MVP Windows Networking. WWW.EZLAN.NET