I'm new to A's too but my horn did this to me last weekend. It turned out to be the button. The internals of the button were all rusty and not making a good ground when the button was depressed. To properly fix this you must remove the light switch at the end of the steering column, 2 bolts, a retaining clip, and then the horn shaft will slide out. I have a truck so I had to dismantle the horn button assembly with the shaft sticking 1/2 way out of the steering wheel. You will be able to remove the unit and put it on a work bench.
The button is held in by 4 tabs. Carefully straighten the 4 tabs and then work the button out of the shaft. If they break, worse case is a new assembly for $39.99. You can probably get away with breaking one or two of the tabs though. The button has a washer, spring, and cap. Put all of these on a wire wheel and clean them well. Also clean the inside of the steering wheel where the horn button washer sits.
While it's out, check continuity of the wire in the shaft on both ends. Put everything back together. Toot the horn and smile.
Before messing with the button, I would supply your horn with direct power and ground to make sure it works. If it works, then go for the button.