Considering when it works you get cols air.
Safe bet that the system itself has no issues.
Judging from your description …
You can skip replacing fuses, they either work or don’t.
Being the system sometimes works, even money that all the fuses are good.
The relay may be a different story, but that is easy to remove and test without having to get a replacement right away.
My money is on a faulty climate control module..
You might try hooking up a scan tool and see if there are any codes associated with it.