I have the above mentioned 2005 Sebring Convertible (2.7L V6, Touring) and the AC will work occasionally, but when it is hot and humid, it is sure to blow hot. First up was to check the system pressure and top off if needed - not the problem. Also blew the bugs and junk from the radiator fins. The wires and electrical connections look good at a glance. Turning the car off and on again doesn’t work. Why would the darn thing work part time and take days off when we need it most?
Have your “clutch cycling switch” checked. This is a small sensor mounted in the air conditioning condenser at the front of the car, at the bottom, near the radiator. (at least it is on my old 94 Chrysler) An intermittent failure of this part will cause exactly what you describe. On mine, the part was around $70, but can be changed in a few minutes. It screws into a Schrader fitting, so the system does not need to be discharged/recharged to change it. It can be tested by jumpering the electrical connector that goes to it.
Another possibility is if you have the electronic climate control, it could be malfunctioning. Before I replaced mine, I used to have to occasionally reset it. On mine, this involved holding down three buttons for about 5 seconds. You should be able to Google the procedure for resetting yours. I’m sure mine is different, as it is much older.