Damage A/C by running when uncharged?
We bought a newly built home during the Winter and were not told that the A/C unit had not been charged until after we'd been running it for several days 6 months later. The unit has not been running properly since. The installer came out 3 months later and said it was low on Freon and the filter was dirty. The following Summer, it again was blowing not so cool air again so we called them out once more (11 months after it was first charged but 17 months after we moved in). Again he said it was low on Freon and the filter was dirty. They offered to fill it up again, but wanted to charge us for it.
Is it likely that the unit was damaged in that few days of running it without it being charged up? If so, what is the likely damage and what needs to be done to fix it?