I'm a network admin for an ISP, and we've been recommending UPSs for the frequent-reboot routers that our customers have. We've found that routers (especially Linksys) have a real problem with power fluctuations that most other systems and devices don't notice. A decent line-conditioning UPS might solve your problems, but a cheap one will suffice.
Also, could be the device is running out of memory, if your ISP is changing the properties of your connection a lot, or you might have a duplex issue causing a lot of retransmissions. . .
Just a couple of thoughts