Clogging is part of nature. Algae and small dirt get in there and get stuck. The finer the pore, the smaller the bubble, the more easily it cloggs. One company makes ceramic stones that can be cleaned with an acid soak, but I won't risk that with your bubblewand.
Snails will slow clogging by eating the stuff on the wand, but some particles come from the airline and get stuck deep within the stone.
How old is the pump?
You could try replacing the diaphram or air filter in the pump. The air filter reduces the crud in the air line, reducing the crud trapped in the air stone. The diaphram affects pump efficiency.
More parts answers, by the pros:
You may consider just upgrading the pump. Bubble walls use more air than air stones, and the smallest pumps are not really designed to drive them. I don't see any specs for this on Marineland's website, and I don't recall any documentation coming with mine, but there's a basic fact that the more bubbles, the more force it takes to generate them. (Granted, my bubble wall is 48" long, so I've seen the more extreme version of your problem.)