Diagnosis
When the ice maker itself quits with no obvious mechanical hang-up, it's usually one of three things: no water getting to it, a frozen fill tube, or a failed thermostat/motor module in the ice maker.
How to Fix It
Run through this checklist. 1) Check water supply: Does the water dispenser work? If not, that's your main issue (see the slow water fix). If the dispenser works, water is getting to the fridge. 2) Check for a frozen fill tube: Open the freezer and look at the plastic fill tube that directs water into the ice mold. If you see ice in it or around it, it's frozen shut. Unplug the fridge and let it thaw, or use a hairdryer carefully. 3) If water is flowing and the tube is clear, the ice maker unit itself has likely failed. You can try a manual reset by lifting and lowering the metal shut-off arm 3 times, but if that does nothing, the module needs replacement.
If That Didn't Work
A less common culprit is the freezer temperature being too warm. It needs to be below 10°F for the ice maker cycle to initiate. Check your freezer temp with a thermometer.
Heads Up
When replacing the ice maker assembly, get the exact model number from the old unit. They're not universal, even within Maytag. The part number is usually on a sticker on the side of the ice maker.