It seems clear that the recent election was the trigger for an expression of deep discontent in Iranian society. But the weakness in the protests has been their reliance on well established figures in the Iranian state. Mir Hossein Mousavi was a prime minister of Iran during the 1980's, and oversaw the execution of thousands of dissidents during that time. Much of what is going on in the elite is a territorial dispute over power, and access to the oil and resource wealth that controlling the state allows. The principle figures are Hashemi Rafsanjani, who was president at the same time Mousavi was prime minister, and current "Supreme Leader" Ali Khamenei, who backs Mahmoud Ahmadinejad. Whoever is on the losing side of this power struggle will face harsh recriminations.
However, the action on the street is only partly about this power struggle. Like all embryonic mass movements, it has multiple grievances and sources of support. As Mousavi has sought to utilize the power of mass protest, he also has been careful to not undermine the set-up of the Iranian state and has called for protesters to do the same. As his statement today read, "We are not against the Islamic system and its laws but against lies and deviations and just want to reform it". However, these type of situations can spiral outside the control of authoritarian management, and new leaders can emerge.
Given today's reports of crowds in the range of 10,000 people, it seems that Khamenei has been able to isolate and weaken the protest movement. Perhaps there is a perception that he moderated his stance during his recent address, such as admonishing Ahmadinejad's debate style, or expressing a willingness to recount ballots. But a good part of it must also be the threats he unleashed during that same speech. No matter how chaotic the situation is, small protest numbers do not act as regime threat. In some ways, they encourage the brutality of the Basij, and that's what we are seeing and hearing about today. Larger protests would render their power moot, since they are essentially state sponsored thugs - not even a militia, which tends to have more organization and a military structure. The Basij , in a way, serve a role as buffers between greater police and military involvement, and preserve the perceived neutrality of this key source of power for the state.
Some have argued that the genie cannot be put back in the bottle. But Tiananmen showed that even a large and relatively well organized mass movement can be crushed for at least a generation.
Sources : 1, 2, 3, 4, 5, 6