The description of what is happening is too vague, is the contactor staying in but the control voltage disappears?
If so, the control may be going through NC contact on the SqD.
Did you wire it from the original or did you come up with the control circuit? What picks up the contactor?
I would imagine it is a standard push button start across a retaining contact on the SqD and a stop button in series?
Sometimes a trip switch drops out the motor when the saw is down.
More is required and preferably how you wired it.