My air handler will not shut off. I hear the thermostat (Honeywell programmable, about 4 years old) click, calling for a shut-off. The compressor shuts off outside, but the indoor blower keeps running. Sometimes if I manually turn the fan from "Auto" to "On" 3 or 4 times, it will shut off.

What's going on?

Disconnect your stat from the sub-base... does it stop?

I agree, good place to start. This could be just a failing stat.