Whats the size of his tank? Is it heated and filtered? Betta's will be lethargic and sickly if in too cold of water, Ideal temp is between 74 and 82 degree. Also a betta needs stuff to explore, when I was younger we had a betta in a bowl with nothing, and it did nothing, and sadly it died young. Now I have a 5 gallon and a 20 gallon heavily planted betta tanks, and the bettas a crazy active.
How often do you change the water? An unfiltered bowl is going to need to be changed almost daily, the ammonia will kill the fish, and the fish will lose color and become lethargic before it happens.
Also do you treat the water before putting the fish in, other than boiling it?
Rather than boiling, use a water conditioner like aquasafe or bettasafe, this dechlorinates the water and makes it safe for the fish.
Betta fish are very active creatures and unfortunately have been marketed with lies and inaccuracies. They are tropical fish and need very specific conditions to thrive. A favorite comparison of mine is just because a dog can live in a cage it can barely turn around in doesn't make it a good healthy environment for it to live in, and thrive in.
Oh and yes bettas sleep, but they don't have eyelids so... yea..
But the water conditions are probably no good, if you can get a water testing kit, not the strips, an actual chemical one, I test my tanks regularly especially if a fish is acting funny.
If a its an ammonia problem all is not lost, create the proper environment and the betta will bounce back and be making bubblenests in no time.
Its really important to heavily research your fish!