My guess is they will now go back to their original diagnosis and tell me I need a rebed for $700 +.
And yet a service guy has also told you that you didn't need to rebed it and did something and it worked fine for a couple weeks.
All water treatment equipment requires maintenance at times. An air pump system requires a bit more and sooner than others because there are more parts, like this first tank and the compressor and the vent.
Look at the bottom of your control valve and see if there are separate inlet/outlet connections where the control attaches to the tank or not. If not then you have an industry standard tank and the valve simply unscrews out of the tank and you could rebed the tank yourself right in your basement in an hour or so IF it needs to be done. You can buy the mineral from Culligan if they will sell it to you or online for much less than they will want. Rather than it being Birm, it may be Centaur carbon of regular carbon. It may be something like Cullex which used to be Pyrolox.
Before you do anything else, get raw water tests for iron and pH. Hardness would be good too, and manganese if you could get it.
Did you read my last reply?
I suggest you study my last reply, print it out or have it on your monitor as you call Culligan and get the manager or the owner of the dealership on the phone and calmly explain the situation and ask how the system works. Ask questions based on my reply and get an idea of what was done on the last service call. Find out what media is in the filter if they'll tell you. Tell him there is no pressure gauge on their system and ask how they can check or adjust the pressure of the compressor without a pressure gauge.
I think I mentioned this in my last reply but, you or they should add a pressure gauge to the air vent tank or plumbing there so you can see the pressure in it.
Ask if there shouldn't be a check valve on the inlet to the vent tank.