The water heater supplies hot water when first taking a shower, but the water cools significantly, and by the end of the 4 minute shower the water is barely warm. It didn't used to be this way, it used to supply hot water the entire time. What would cause this?

I forgot to mention that this is a State Select gas water heater.

Possible broken or deteriorated dip tube. Remove several faucet aerator's. Look for small, granular, plastic like particles. Would indicated deteriorating dip tube

I think Harold is heading in the right direction but we won't know until you can back after removing the aerator. A dip tube isn't that hard to replace so we can help with that.

Weren't State heaters in a big dip tube recall a couple of years ago? Could get a free one-dip tube that is.

Also inspect the burner assembly. Severe build up on the burner will create a oddly shaped low orange flame that will leave the burner constantly firing without adequately heating the water.

Not just Select, pretty much everybody White Particle Warning From Dip Tubes - www.diptube.info - Another great official website from Michael Leavitt & Co Inspections, Inc. Worth calling Select if it turns out to be your tube. Read the article about how to test the white particles if you find some and it also says some manufacturers do give a free tube and some $$ for the plumber

Some small plastic part. In the bath. H20 faucets. I did a draw-down test as on State's website, and the H20 dropped over 30 deg. so it could be a dip tube, but after removing the comp. fit. I couldn't unscrew the pipe to the H20 heater inlet.