This could be the classic symptom of hard disk failure, or soon-to-be failure. Can you still get it to restart when you disconnect/reconnect AC power? If so, and you value the recordings on your Tivo, you may want to act fast to replace or upgrade that hard drive. But try these tips first:
*** Note that problems like this can also be caused by AC power spikes or fluctuations. Your Tivo is essentially a computer inside, so you should seriously consider powering it with an uninterruptable power supply (UPS). Good quality 350VA UPS's are available for well below $50 and will power your Tivo for nearly an hour, plus they provide much better powerline isolation and protection than a surge protector.
*** Check your Tivo's internal temperature. If it's running too hot you'll sometimes see problems like this. Look in "Messages & Setup" -> "System Information" and scroll down a couple of pages to see the internal temperature. Anything under 50-deg C is usually OK. If it's higher than that, make sure you have good airflow under and around your Tivo. It's a good idea to raise your Tivo up an inch or so for better airflow. Some folks use pop bottle caps under each corner.
*** If your Tivo is a combination DirecTV+Tivo receiver, you should try re-seating your access card. Remove power, remove the access card, wait a few minutes, re-insert the access card, and reconnect power.
*** If you're comfortable opening up your Tivo (which will void your warranty if you still have one), then disconnect and reconnect all the cables leading to the hard drive(s). Sometimes connections can work loose, or tarnish, and re-seating them will help.
*** If these steps don't help, then it's likely a hard drive problem. You can try a "Clear and Delete Everything" (in the Tivo's "Messages & Setup" menu). That might help the drive repair itself, but you will lose your recordings, Season Passes, and other settings.
*** Finally, if all else fails, then you might want to try connecting your Tivo drive(s) to your PC and run the disk manufacturer's DOS-based diagnostic utilities. These are usually available for download from their web site. Unfortunately they don't always detect all of the failures that can disrupt your Tivo. Some folks have reported success using the SpinRite disk repair utility available from Gibson Research at http://www.grc.com/sr/spinrite.htm
or HDD Regenerator at http://www.dposoft.net/#b_hddhid
Also check out these sources of information, much of which you'll find in the Tivo Underground Upgrade Center forum: