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Possible bad connection on a ground or positive which needs the extra amps to push through. Possibly an starter relay if the vehicle uses one. II would first try to see if there is a draw on the system by disconnecting the negative post and then using an amp meter in between the post and cable measure the current with key off. Should be less than .1 amp. Also trying another battery would be one way to verify that isn't the issue and finally i wouldn't take one shops diagnostic as gospel. A worn set of brushes in the starter can give this same symptom. It might pass some test they are doing but if its an old starter i'm changing it out.