Could just be low on refrigerant. Easy to check with a gauge.

 

Assuming it's like in the mid 80s or higher there, if it were very low on refrigerant it wouldn't be able to get satisfyingly cold in the first place.
Need more info.
Year of car?
Trim level?
How many miles on the car?
Any work done to the AC in recent years?

What are the vent temps while it works correctly (gets cold)??
What other things do you notice when it stops cooling? Fan still on full blast but airflow from the vents decreased or quit completely?

When it stops getting cold, you need to get out open the hood and do some checking:
Did the compressor clutch stop engaging? Does it cycle? Is it on continuously?
Does the compressor continue running, but airflow from the vents slows down and stops?
Are both radiator fans still running whenever the compressor clutch is engaged?

 

We had the same thing happening with our daughter's Fit. It would blow ice cold air when you first start the AC, but after about 15-20 minutes of driving the air will be warm. When it happen while I was driving her Fit, I stopped and open the hood and looked at the compressor. I could see that the pulley was turning, but the clutch plate that engages the compressor to the pulley wasn't turning. Ther AC switch light was on, so I figure the magnetic coil that grabs the clutch plate was either too weak or the air gap between the clutch plate and pulley was too great. I took a long pry bar and gave the clutch plate a quick tap (*do this at your own risk, I am not responsible for any injury to yourself or damage to your car if you do this) and immediate the coil grabbed the clutch plate and the compressor was spinning. Cold air started to flow from the vent. Upon investigating this I found out that there is a shim behind the clutch plate that is used to adjust the air gap. Jack the Fit up on the passenger side, removed the wheel and removed the plastic access cover. With the cover removed, I could get a socket and my cordless impact driver to remove the nut that secured the clutch plate to the compressor. I found a really thin shim behind the clutch plate. I reinstalled the clutch plate back without the shim but first making sure that I could spin the clutch plate once it was secured.

The AC has been working fine ever since. Cost of repair $0.00. There's a Youtube video by South Main Auto on a similar repair to a Honda Civic. If you find his video give him a like and subscribe to his channel.

Here's a link to the Youtube video.


Good Luck with your repair and hope it is as easy and cost effective as it was on our daughter's Fit.