You haven't stated at what speed it doesn't work. It probably is either your low or high blower relay. If it doesn't work at all it probably is your switch.
There is a TSB (technical service bulletin) out for this year model with this particular problem. Seems this is due to a faulty ignition switch. Contact a Mitsubishi dealer service department and ask them about a TSB on the radio/fan blower working intermittently.
If the fan is on top where it can be accessed under the hood,it may just need leaves and trash cleaned from around it. You need to raise the hood and take the vented cover off(this should be located on the passenger side)just under the wiper. You should be able to insert your hand and clean out.