DIAGNOSIS The router is likely overheating or experiencing a power supply issue. This model can get toasty, and its auto-reboot is a safety feature.
FIX First, check the placement. Get it off the carpet, away from other heat-generating gear like a modem or game console, and make sure all the vents are clear. If it's in a cabinet, take it out. Next, check the power adapter. Make sure it's the original one (model PSADP12V2A) and that the barrel plug is fully seated in the router's port—it can feel snug but not be all the way in. Give the router a cooldown period by unplugging it for 10 minutes.
IF THAT DIDN'T WORK Try a factory reset. There's a small recessed reset button on the back. Hold it down for about 10 seconds with a paperclip until the power LED blinks amber, then release. You'll have to set it up again from scratch, but this can clear a corrupted firmware state causing reboots.
HEADS UP If the problem persists after a reset and in a cool location, the power adapter itself might be failing. Borrow a known-good 12V/2A adapter with the correct polarity (center-positive) and barrel size (5.5mm x 2.1mm) to test before buying a new one.