Replaced blower motor and seems to be working good!!I'm thinking that was the problem

 

Replaced blower motor and works good!I think that was the problem

 

My 2008 grand caravan blower cuts off randomly also. As soon as I turn off the engine and start it back up, the blower will come back on. Is it something in the ignition wiring?

 

In your case it's more likely the TIPM. Not clear from the wiring diagram but it either controls power or ground to the blower motor. The TIPM has been a headache for Chrysler causing various electrical problems and may go back order when ordered. Try tapping on the TIPM (fuse box) and blower motor (under dash passenger side) to induce the problem.