AOL used to timeout back in the day because they used to charge by the minute and people wouid get pissed if they forgot to shut it uoff. anyone remember payin gfor internet by the minute? what a pain!
my internet frequently quits working, but it isn't the fault of the ISP. in fact, there's still a signal coming in on the modem and visible in the network connections box similar to the original poster's problem.
my problem lies with a cheap router.
the original poster didn't describe what type of connection he has or whether it's connected directly to the computer or via a router so I guess mine is yet another random guess at the issue.
instead of restarting the computer, try just resetting your router next time and see if that works. if that's the case then your router is at fault.