I replaced the fan, motor and the capacitor on my old Kenmore condenser unit. The unit runs well, and cools the house properly. Unfortunately once it cuts off, the motor will not turn unless I jump start it by turning the fan with my hand. Once it start again it runs fine and cools the house propely. It seems as if it once it gets hot it will not start by it's self

Start winding is damaged, replace the motor and capacitor again

How long ago did you replace the parts? How long before it petered out? Might consider changing out the capacitor first and seeing if that's a fix before investing in a new motor. For most anything you do, use new parts -OEM if possible. Make sure cap and motor match.