Clerics don't need rest to replenish spells, they just need to wait until the appropriate time of day. So by the book, if your cleric had enough spell slots to fill up with cures and restores, you could theoretically go without sleep forever.
My own house rules for lack of sleep are a bit more harsh, and they go like this:
If you stay awake for one full night, you must make a Fort save (DC 15) or become fatigued. For each additional night, the save DC increases by +5. (Staying awake for more than 48 hours is extremely hard.) Magic can temporarily remove the fatigue, but it comes back eight hours later unless you have slept in the meantime.
After failing two nightly saves, you become exhausted. Again, magic can help, but only temporarily. Four hours after being cured, the fatigue returns; four hours after that, you're exhausted again.
Fail a third save, and the mental effects start. You take a -4 circumstance penalty on Will saves, and on any skill checks that require concentration or patience. Each round you are in combat, you must make a Will save (DC 10 + 1 per sleepless night) or act as if
confused. In addition, you must make a Fort save (DC 15) once per hour, or fall asleep despite your intention to stay awake. Magic doesn't help with these effects unless specifically designed to remove or lessen your sleep requirement.
If you get 4 hours of sleep in a 24-hour period, you must still make the nightly save, but its DC does not increase that day. If you get 8 hours of sleep, you move to the next less-serious step of the scale, and you need not save that night (but the DC remains the same for next time). Once you have had sufficient sleep for the same number of nights that you went sleepless, or have spent one entire day resting and sleeping, the DC counter resets and you're fully back to normal.
This all is modelled on my own experiences trying to go without sleep for days at a time. (I'm a programmer, we is stupid that way.

) It's not medically precise or anything, but it's about as close as I could get within the rules.