I have an air gap installed under the counter apparently because the previous owner did not want to drill through the granite counter top. Recently water has been draining out of the air gap and collecting in the bottom of the cabinet. I'm not sure how to fix the problem. If I have a hole drilled through the counter top the water will then spill out on the counter, not in the sink because it's an under-mount sink. If I remove the air gap I am then creating a code violation. Any suggestions?

Does water back up in the sink? If not, clear the hose between the air gap and the drain. If water backs up in the sink when dishwasher is draining snake the sink drain line.

Hi dkbsf and welcome to The Plumbing Page on AMHD.
You piggybacked on a 2 year old dead thread so I gave you one of your own. Before you post look in the upper left hand corner for the date..
Your complaint is why I never recommend installing a counter top air gaps. Simple reason, They fail and leak. We install high loops,(see image) in my area with never a problem.
You should remove the old air gap and run a high loop air gap.

Install the drainage hose with a large loop between the point where it discharges from the dishwasher and enters the sink drain. Think of a bell-shaped curve. Make sure to attach the drain hose as far up in the cabinet as you can, using hose clamps or a pipe strap to secure it, when you run it between the dishwasher and the disposal. Good luck. Tom