If you do happen to get stranded, talk to the owners/operators of the field as soon as possible. Explain that your plane might be stuck there for a few weeks while waiting for parts, and try to find out how you can make that happen with the lowest cost for you, and the least hassle for them.
If they know you're not going to fly for a few weeks, then they can stick you in a back corner of some far away hangar, not occupying prime real estate near the doors of the most popular hangar for instance. Or they may reduce your fee by parking outside, or even on grass instead of tarmac.
Heck, in some places hangars are rented out as a whole to certain groups - for instance a group of homebuilders. The airport authority doesn't have any say anymore as to how that hangar space is used, but they may be able to point you to their representative, so you can try and arrange something with them.
But yes, as far as I'm concerned they have the legal and moral right to charge you a parking fee.
Last edited by BackPacker; 9th Dec 2014 at 13:12.