I knew a "clockie" who swore by putting the movement to boil on a stove in a pan of soapy water, and you should see the muck that comes out! I suppose todays equivalent would be an ultra sonic cleaner, and then carfully examine the side plates for any wear at the pivots, if they all look reasonable, all well and good, carefully and minimally oil the pivots and the spring (if it has one) and then set it op on a bench and run it. As said above, usually dust and gummed up oil that stops them, but if there are worn pivot holes, they can be bushed.
Phil