The relay contacts are most likely wore out, so sometimes they work, other times they don't.
When the grinder fails to start, do you hear/feel a click in the relay just as you power the grinder up? If so, then the relay tries to work, but doesn't due to the worn contacts.
The relay has three wires on it. 1 in, two out. Of the two out terminals, one goes to the starter winding, the other to the main winding.
You can put a volt meter on the neutral wire, and the other probe on the terminal going to the starter winding. Set meter for 200V AC (or whatever the suitable range is on your meter).
Power up the grinder. You should ideally see 120V AC reading on the meter, but might be less due to worn relay contacts. If the grinder turns and starts up, you'll see it drop to 0V within a second or two. If the grinder fails to turn, you'll probably see 0V or at least a very low voltage. This means the relay isn't passing the voltage, again due to wore out contacts.
Here's the data sheet for the relay, btw:
http://www.sensata.com/download/4cr.pdf
Basically, odds are 99% it's the relay that's just wore out. A intermittent connection in the start winding is also a possibility, but highly unlikely.
You can bypass the relay temporarily to see if the grinder starts up that way. Just unhook the wire that goes to the start winding and hook it to the incoming line wire. Flip the switch, and it should start spinning. Don't leave it running like this, though, as you'll overheat the start winding.
You can hold the start winding terminal to the hot line while switching on the grinder, then once it starts spinning, remove the start winding terminal from hot. At this point it's okay to leave it running.
Don't electrocute yourself.