As you and TigerJimmy said, air conditioners run at full capacity or zero capacity. There is a maximum amount of cooling that it can do. Apparently air conditioners in the US are sized to provide about 20° of cooling, so as to not cycle too much. You don't want your AC to pump 32° air into the house for 30 seconds and then have to do it again five minutes later. You want it to pump 65° air for five minutes and do it again twenty minutes later.

I guess what I want to know is: is there anything I can do to make the unit cool down more – 25° would make sense here – or do I just have to replace it?