That if its droping fairly regularily like that.. its LESS likely a signal issue, etc.
(started off thinking it could be a more street /time of day issue.. but not if its that much consistant)
Now when you are saying re-plug the cable.. is this the cable INTO the modem? The network cable to the PC? Are you rebooting the modem or just doing the unpluging.
Have you swaped the cable from the modem to the PC?
IF you were to switch providers.. you would need to check with WHO you are going with. DSL goes over the phone lines (but often is much slower speeds down/up than cable).
Another provider, over the cable... if its something signal wise or something in the end, could have the exact same problem.
(if its not say a back end issue, etc).