To be clear here, does your AirPort gadget (in the top menu bar) say you've lost your wireless connection (it goes all gray), or do you lose the ability to connect to the Internet. Two very different situations cause these different issues.
Also, whose DSL are you running (AT&T?), and how long has this problem been happening? Did it work for you for a while and then suddenly change? Did you change any hardware, like get a new modem or replace your router? Which Linksys router do you have? (The router's hardware and firmware versions would be helpful too.)
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