these Poole clocks are fairly robust clocks and in MHO relatively not very finicky! Make sure the battery terimials are clean (your already on this), and the contact switch is clean.
Hopefully no one has gave it the WD40 treatment at some point in its life, as these clocks are a bit of a workout disassembling, cleaning and reassembling! They riveted the plates together and you'll need to drill and tap the posts for a complete overhaul! Oh and these movements do not need the pivots oiled, though I wipe them with oil personally!
Oh, there's much debate on a well running clock will rewind, lifting the weight. My feeling is as long as the roller is free and not dragging it should rewind about every 20-30 pendulum swings!