First off, if you do disconnect the router for a test, does it work properly connected directly to the cable modem? We need to isolate this issue to the router, or some other cause. If it's really the router, try the following fixes.
Some things you can try here.
- For wireless connections, change the channel on the router, I like channels 1, 6, and 11 in the US.
- Update the firmware to the latest version available on the manufacturer's site.
- Reset the router to factory defaults and reconfigure.
Many times these measures will resolve a lot of intermittent issues.