Have to say that low gas is normally the reason for aircon compressor not being engaged as it is a safety device to stop compressor damage.
...or over- gassing, the pressure switch is two way and protects the pump from over filling. Did you get a report indicating the quantity of gas and oil put back into the system? It should match the quantity on the sticker under the bonnet, and I know they do get it wrong on occasions... particularly with some of these fully automated recharging stations.
Culzean's post is spot on, check to see if the clutch is operating first. If not, then gas pressure is too low/high, or there is a fault with clutch, associated wiring or a system sensor - a diagnostic might be the way to go. It will tell you if anything is preventing the system from running, or if the system should be running.
The initial symptoms of not running when the engine was cold did point to borderline low gas, and you seem to have gone from working sometimes, to not working at all after regassing?