OT?...How does gravity vary?

Try a horizontal pendulum. It would be independent of gravity.

Yes. Sometimes the heavy gravity sits as a layer on top of the light gravity and holds it down causing a gravity inversion layer.

Gravity varies a little bit due to the effects of the sun and moon (which is why we have tides) but I doubt that this is the reason for your clock stopping.

Gravity also decreases with increased altitude, and is slightly different at different places on the Earth's surface due to different local geology.

A gravitational force of attraction exists between any objects with mass, so in theory moving any object would cause a change in the total gravitational force seen by the pendulum. However, the Earth is very large and close, so most other things will not cause any detectable change.

I don't think variations in gravity are stopping your clock. I have one that has been running on one AA battery for about 2 years.

The pendulum needs to be aligned not only in the lateral plane (side to side so that it swings equally to either side of the solenoid mechanism), it needs to be aligned fore and aft so that the pendulum's bearing (usually some sort of blade or wedge shape) makes contact with its rest with minimal friction.

And when teenage boys watch p*rn the reverse seems to happen in their pants!

Nope! No observable reason for it to stop other than dirt accumulated in the bearings due to (too much) oil. The force of gravity changes with locale; known to be stronger near large deposits of iron. Extremely doubtful of local "modulations", and the variations mentioned above are very small.

As the hippy would say, "Heavy, man!".

Hmm. I thought that was due to the gravitational attraction to satellites passing overhead.