Ok, a couple things could be causing the problem.
The First place I would start is making sure your Network Card isn't killing the connection when it goes idle. This is a power setting on your network card.
Go to Device Manager ---> Network adapters and select your network card properties. Select Power Management and set it to not reduce or cut connection in system idle.
Also, I would adjust your Network Card's Link Speed. This is found in your network card properties aswell under "Link Speed" (or a similar name). The current / default setting for Speed and Duplex should be Auto Negotiate. You are going to want to change this to 10mbps Full Duplex. If this solves your problem, then wait a day or so and bump this setting up to 100mbps Full Duplex and see if your problem stays away.
Chances are both of these things are working together to cause your problem. You modem and or router probably don't like Vista negotiating the link speed and will be happier with a standard setting like this. Plus, you network card is probably reducing the connection during system idle while vista is still auto negotiating and this is probably causing your network connection fail.