So a dictator has to deal with demonstrations somehow. If they continue indefinitely, they disrupt the usual business of the country and make the regime look weak. Right now pretty much everything is shut down in Tunis and Egypt (at least around Cairo). The dictator might be able to discourage the demonstrators, perhaps through intimidation and capturing public support from a larger part of the populous. Or he might employ stronger methods, like deploying riot police with tear gas, and arresting the biggest troublemakers. If that doesn’t work he can deploy the army, even possibly ordering them to open fire on demonstrators. But those orders only work if you have a military or police force willing to brutalize their own countrymen. If they instead allow the demonstrations, then essentially the dictator has no power. How can he rule a country if nobody will listen? Eventually someone will be able to forcibly remove the dictator – perhaps an officer who commands greater loyalty than the dictator in his unit. Or maybe a group of ministers who want to overthrow the dictator for their own gain. Of course, the smart dictator will flee before this happens.
Right now, in Egypt, high government officials are sending out all sorts of orders to try and shut down the demonstrations. Demonstrators are ignoring the curfews, and military units stationed there are doing nothing to break things up.
I just heard a revealing anecdote about a BBC reporter who just arrived at an airport in Cairo. Apparently the airport security is under orders to confiscate all equipment from reporters and journalists. Senior officials are attempting to enforce this, but most of their underlings are ignoring or completely flouting the order. So one guy in charge will manage to take away a few cameras, but then someone else just gives them back.