A sticking tap handle is almost always caused by drying beer residue plugging up the works.
To see why, you should disassemble your beer faucet and you’ll see that a long shaft rides back and forth in the bore of the faucet and beer is shut off with a seal that closes in the back of the faucet. When you pour a beer this shaft gets wet with beer then the beer that’s left on the shaft dries into a sticky goo. Once this sticky goo gets thick enough the shaft starts to bind inside the bore of your faucet causing your tap handle to stick.
Bars and pubs rarely have this problem because they pour more beers per hour than you pour in a day and the constant flow keeps the beer residue from drying into a sticky goo. The solution to the problem is simple – just purchase a small trigger sprayer, the type some people use to mist houseplants, and fill it with cheap vodka or gin. Then place a bar rag under the mouth of your beer faucet and spray the heck out of the inside every day or two. The alcohol in the vodka will kill anything trying to grow inside the mouth of your beer faucet and the water will flush out any drying beer residue.