A Nylock prop nut should stay put. If it doesn't, it's worn out and you need a new part. A loose prop nut can cause the prop to vibrate more.
 
The banging of the prop back and forth can chip gears inside the lower unit. In some instances, the nut can back off and result in lost props. 
 
You should tighten the prop nut to around 55 ft-lbs of torque until a flat nut surface is aligned with a washer tag. You can then bend one tab up on either side.
 
You should not reuse an old worn-out prop nut. Once a nylon lock nut is installed, the nylon insert is deformed; if you were to remove the nut and reinstall it, its locking strength would be lost.
 
Part Numbers:
11-52707A 1, 11-52707Q 1, 11-827614
 
Includes one (1) Brass Nylock Prop Nut.
 
Contact Mike Hill at STVracer@yahoo.com with any questions