Question : Problem: Sudden loss of wireless internet connection

We have a linksys wireless system with a BEFSR11 router which has worked fine for the past year. However, suddenly, we lose the wireless signal then it kicks in again and then off again.

What could be going on and what kind of troubleshooting should I try?

Answer : Problem: Sudden loss of wireless internet connection

What is your wireless router model?  The BEFSR11 is a Cable/DSL router, but does not provide WIFI.
1) I would do as philippe7v7 suggested and backup the settings of your WIRELESS router.
2) I would check with the manufacture's website for any firmware upgrades for your wireless router.  Download them and upgrade your firmware thru the router's admin page.
3) If you are still having troubles, I would read up on DD-WRT firmware (dd-wrt.com) and see if your router is supported.  I highly recommend DD-WRT firmware; it has solved problems with fickle wireless routers for me before.
4) What is your signal strength when you lose connection? Perhaps positioning your router away from interference or signal blockers could help you out.