I have a 03 Matrix and my AC compressor does not stay on long enough to cool the car. In cool weather (less than 80 degrees), on the highway, the AC works well enough if I have it on high. When the weather heats up or when the car is sitting still, the AC doesn’t work at all. Today, it was in the 90s and I got an occasional cool breeze from it, when the car was moving.
When observing the pump, I see it kick on briefly then quickly turn off. It’s off much more than on, when the car is sitting still. The coolant pressure is charged and I tried swapping the relay. For a time, it was making some noise. I would kind of make a rapid dove sound when running and a fart sound when shutting off. I didn’t notice that happening today though.
Are the engine compartment fans working properly? The fans aren’t needed when driving fast usually, but they must be working at lower speeds and at idle, otherwise symptoms will appear. I think an engine compartment cooling fan not turning on when it should, or not running at the rpm it should, could cause this symptom. Checking the engine compartment fan operation is probably where to start.
Sounds like you are low on 134, there are kits at stores to recharge your a/c but they can do more harm than good. I would recommend finding a shop to inspect the system charge and look for leaks.
My vote is with db4690; it sounds like it’s short cycling. The use of the word “coolant” is incorrect and can point to a lack of knowledge about A/C system.
Someone with a good understanding and experience in automotive A/C could probably tell you what is happening with nothing more than his eyes, ears, and fingertips. But for most people, with the symptoms you describe, the next step would be to install a set of gauges and report back the findings.