Unless your pump motor uses direct current instead of alternating current, it has no brushes.
Try connecting the pump directly to a power source instead of through a timer.If it works fine check the timer.
Another possibility is that the pump has a short circuit inside.If you are using thermal circuit breakers instead of ones that trip off, the pump comes on again when the thermal circuit breakers cool down and re-establish a contact.

thankx for the responce. the motor just does'nt shut off. it kind of slows down and then shuts down all together.when that happens, there is a humming sound coming from the relay.after awhile though,it will start up just for about the same time though.

If I read you right, your pump motor seems to have one of those centrifugal contacts for the starting coil(capacitor).
When the motor is switched on it runs initially on the starting coil, which is connected through a set of contact points on a centrifuge.
Once the motor builds up speed the centrifuge causes the contact to break and then the motor speeds up.
If the contacts are stuck for some reason,the symptoms would be quite similar to what you have given here.