The odds are that it shouldn't, assuming you have a reasonably new router and if your using windows that is has all service packs loaded and updated. I would recommend rebooting it (unplug for 30 seconds then plug back in). If a reboot doesn't work, try resetting it. There is a tiny little reset button that is usually recessed and you need a small item like a paper clip to press. A quick and proper google search of your router model should produce a quick guide on where it is located as well as some quick tips on resetting it. You will have to set everything back up again after that. If your still not having any luck, you could try flashing the latest firmware and then do a reset for about 30 seconds. Some Linksys routers are known to kick off users for all kinds of quirky reasons, so it is most likely not your computer or TB. Before I started using my Airport, I had a linksys for years and it (they) needed resets about twice a year for disconnect and DNS issues (unable to connect to certain sites for no reason).
Hope this helps you out!