OK - is this what you are saying - your having some problems with your router, and everytime you have problems with the router, you lose your Internet connection. Then, to get Internet back, you reset the router? Am I right so far? And then you are asking if the firewall could be causing this?

Well, first of all, what kind of router/firewall/network configuration do you have running? And what are the difficulties with the router? Is it losing power, not routing packets, etc?

If your firewall is not configured properly, then it could be causing problems, but my first guess is that your problem isn't because of your firewall. It would help us to have some more information...