"Before I went to the Antarctic Peninsula in January 2000 there was great public concern about the hole in the ozone layer growing like a mushroom, [...] Ukrainian scientists who have monitored the hole for 9 years have found little change if any in that time. So much for the scare mongers. "Umm, that would be because we spent over 20 years hammering out international treaties to stop production and release of CFC's and other ozone depleting gasses, and spent truck-loads of cash developing ozone friendly alternatives to CFC's so we could still have refrigerators when we stopped making/using CFC's. What did the correspondent think all the "CFC-free" stickers on aplliances were for? While we have succeded in reducing ozone depleting chemicals through this massive international action, ozone levels are not expected to recover to 1980 levels until around 2068.
See here for a general history of the ozone hole and our understanding of it, and here for a graph that shows ozone has indeed stabilized, at exceptionally low levels.
Image Source NASA.
Yes, the ozone hole has stabilized because we did something about it.
The general trend seems to be this. Scientists/engineers/medicos discover a serious problem. Scientists/engineers/medicos convince politicians something needs to be done and then work feverishly to fix/avert problem. Problem is either averted or greatly reduced. A few years later, John Q Public says 'What about problem X? scientists/engineers/medico's had their knickers in a knot about this, but nothing happened. They are such scaremongers!"