Any AC unit can be regassed without a problem even the old R12 gas can be replaced with one of the newer ones that is more friendly to the atmosphere.

But you main question was the AC not getting cold and then a few days latter it got better. Most likely some gas has escaped from the system this normally happens through the compressor seal if it isn't used all that much or left not running for long periods of time that is the AC not the car. Now provided that everything is OK all that should be required is a top up of the gas and just about any repair shop will be capable of doing this without a problem. But and here is the big one if the AC has not been serviced for a long time the receiver dryer should be replaced to stop junk getting circulated through the system and destroying the compressor which is expensive compared to the receiver dryer. If you are told that the receiver dryer needs replacing don't skimp on this as it is the cheapest insurance possible to protect the compressor.

What they should do is remove the gas and oil from the system and filter it so any contaminates are removed then crack the lines and replace the receiver dryer {the round tank shaped thing generally black with a clear round opening on the top and sometimes with a pressure switch screwed into the side.} They should also replace any seals that may be there and then evacuate the system and put in a small charge of oil/gas and test for leaks the current crop of oil used fluoresces under the right light and you can see a green stain where any leaks are or they run around the system with a sniffer not as reliable but still effective.

Generally most gas leaks out the front seal of the compressor after long periods of no use as the seal drys out and can no longer keep the pressure in, but from your description there doesn't seem to be much of a problem and a top up should keep it getting cold very quickly.

Col