This page is designed as an aid for people who run continuous redstone circuits. These methods work best on small circuits that run in loops, i.e. 4/5 clocks.
Currently, there is a glitch involving repeaters. In singleplayer, when you save and exit, and then come back, any repeaters that were running in a continuous circuit will freeze. A block directly next to the repeater must be "updated" to jump start your circuit. This also appears to happen in multiplayer, if the chunk is unloaded from memory.
This problem has been mostly fixed in singleplayer in 1.0.0. Although, it may still exist in multiplayer, which these methods should still work.
EDIT: This glitch still exists. This can happen in certain redstone setups. The repeater sometimes gets locked to on, and you have to break it to fix it. This has been tested on a modded 1.8 client several times, and the same thing has happened.
Change at least one block that is adjacent to every repeater that you want to refresh. Or you can update Minecraft to 1.0.0 which might solve the problem.
Method: Automatic reboot using a minecart
This method uses a small circular track with a detector rail, powered rails and some regular rails. The powered rails must always be powered. The detector rail should be next to some redstone going to the side of the repeater (read: not connected to the circuit). When the minecart activates the Detector Rail, it will fire the redstone signal and launch the repeater due to a block update next to it.
Method: Reboot using a lever
Place a lever beside the repeater that's frozen. You just need to toggle the lever every time the circuit freezes to reboot the circuit.
Method: Reboot using piston(s)
Place a piston on the block under a block beside every repeater and wire them all to a "reboot" button. When you push this the block updates will reset them all at once. It is recommended to have it reset every repeater to get a simultaneous restart of all systems. This is a handy method for advanced computers because it restarts everything at once, and will cause less glitches. The only downside is the extra space required to wire up the pistons without powering the clock with the "reset" button.