well there could be 2 issues,
1. your router is broken somehow.
2. your router is wrong configured.
we go with option 2 first.
check if your router has a new firmware.
reset your router to default configuration.
then power down modem and connect router to the modem.
make sure router is set to automatic DHCP.
normally it should be if it's reset but check to be sure.
then power down router.
turn on modem and wait till all light burn,
then turn on your router and see if you get a ipnumber from the modem.
and do some tests if you can keep your connection alive.
if you're still getting issues then i suspect that your router has some kind of error.
then the only option would be get a new router,
but try to get a decent brand.
if reading true the forum you read allot of people having issue with sweex, sitecom, d-link and more of those elcheapo routers.
even that every brand has good and bad products.
i use a linksys WRT610n and i must say i'm really glad with it.
if you don't need a gig lan, dual band radio and a usb port you can use for a external drive and make a network drive of it then the WRT160n would be a good option.
another good 1 would be a the new linksys 320 i think that 1 has a gig lan if needed.