While expansion/contraction is, I think, bound to be involved, I think the
biggest problem in our case is movement of the different parts of the door
relative to each other. The paint, btw, is Buckingham Green from
International.

Hi,

The wood won't move more and more, just in cycles, I'd just paint it
when it's dry as possible, and use a paint that's more flexible.

If the gaps now are an eyesore, I'd try masking off and filling with
paint.

cheers,
Pete.