had a escort (don't laugh, it was a good car for the most part) that did that... the starter/selenoid was going out.... it couldn't generate enough torque... we cleaned up the brushes and replaced the selenoid... and worked like a champ after that!
not bad for a car that I traded a broke -ass chevy truck to a guy and got the car and $500 bucks for!! I got the better end of that deal... the selenoid was all of the work I ever did to the car and the truck stayed in the shop for weeks on end!