Periodical refresh of remote file

This isn't possible because the original URL isn't even saved. FileField Sources is just a way of getting files into the field, it doesn't record any additional information.

do you see any potential for this module and this feature?

Adding this functionality would be significant departure from the functionality currently provided (and completely separate in implementation). So I do not think this will be added. If you're looking for a permanent external file storage, look into using Link module and some of it's advanced formatters provided by CCK extras.

True. Something like link + a local cache feature would do that.
I've experimented with that idea before now. Certainly needs the remote resource to be treated as more of an entity (ie, 'node') with 'last updated' and a 'refresh schedule' than would appropriately fit into filefield.

So set up a node that synchs with your source, then use node_reference to refer to it.

Either way, this is going to likely be a full-fledged widget (or even a dedicated field). FileField Sources is nothing but an enhancement on top of existing widgets, with no additional DB storage.