Basically, rebound insomnia occurs when a patient stops taking a soporific drug that he's been taking steadily for some time.
Patients with insomnia sometimes take drugs like
benzodiazepines or opiates to help them get to sleep.
At first, it'll work wonderfully, and the patients will drop off to sleep
without difficulty; over time, though, they'll build up a tolerance to
the drug, and they'll notice that it's not working quite as well.
Eventually, their insomnia will return and they'll be back to square one--and
if they keep taking the drug at the same dose, their insomnia may continue to worsen.
In this situation, patients have a few options, and they're all bad.
First, they can start taking larger doses. This just
exacerbates the problem I described above, so if this keeps up, the patient
winds up taking near-toxic doses of Valium (and probably ends up suffering from
the concomitant side effects as well). Second, they can stop taking the
drug. Now, remember that the patient is now mildly insomniac with a
soporific in his system. Guess what happens when you remove the
soporific? That's right--now he really has trouble
sleeping. That condition is known as rebound insomnia.
This iatrogenic form of insomnia is difficult to treat; it's much
easier to avoid getting it in the first place. Doctors therefore avoid giving patients Valium or similar drugs for more than two weeks straight. | 
