The Iranian leadership know full well how tenuous their position is, it's not just young people in Tehran. After all, one of their biggest embarassments came from someone who was a co-revolutionist with Khomeini during the initial uprisings in 79, who turned around and accused the regime of simply being a copy of the one they overthrew, and was ostracised for saying so.
It's not a question of Faith that has stopped the revolution towards forming a free Islamic state, it's fear of the bloodshed, but it is only a matter of time before the pressure cooker blows.
Edit: The important part is that no-one else get involved, Iran became its own country for the first time in 200 years in '79, and any thoughts of other countries interfering with that will hinder things far more than help them.