Did you reboot both computers, are they both running Adobe CS3?
Please, as Stuey recommended, perform a complete network reboot. Shut down all computers, as well as any other network nodes, (printers, PS3, Xbox, etc.) Shut down the router, and then shut down the ISP provided device. Then bring them back up in reverse order, one at a time, making sure to allow each to completely reboot monitoring the device lights until each become steady and green, indicating that the boot process for each has been completed. Leave off any devices you don't need right now until you can resolve the issue with these two computers.
Are you sure that both computers become disconnected from the network at the same time (or is it possible only one of them)?
When the event occurs, can you use the ping command from the command prompt to attempt to ping the inside edge of your router from either or both computers?
Does the event only occur when you are transferring files between these two computers. In other words, can you jump on the internet with each or either computer and successfully download files of any size without issue? If the answer to this question is yes, then your issue is almost certainly some type of local software that is misinterpreting local node to node file transfers as a network intrusion.
Again simply disabling or attempting to turn off an internet security suite is often not a viable solution as parts and pieces of the application will still continue to run in the background and often you will find that a complete uninstall is the only thing that will produce results.
I do not ever bash anyone's choice of anti-virus products as I'm sure they all have their good points as well as bad points, it's just that I've spent literally hours trying to resolve these types of issues, only to find that something as simple as a failed, complete uninstall of a previous anti-virus product like Nortons had left remnants of the software still on the machine that resulted in problems that only downloading and running their proprietary uninstaller finally resolved.
All though you wouldn't think so, by reading this forum, Windows 7 is, as Stuey mentioned, generally straight forward and simple when it comes to networking, but is extremely finicky about networking hardware and device drivers and can apparently be crippled by various types of third party software that is not entirely Windows 7 compatible.
After re-reading Stuey's post, he didn't suggest rebooting your router, his suggestion was to reset the router which involves using the reset button usually on the back or bottom of the device, that of course would reset everything back to factory defaults, which may not be a bad idea. Of course make sure you have notes as to how to reconfigure your connections.