Many stores that sell a variety of appliances carry one or more models of under counter ice makers. Home Depot has one on their website for $949, but most models run more than that. Sears carries several models, including a KitchenAid one.
Nextag makes many under counter ice makers, and accommodate for any individual. These under counter ice makers can be found at http://www.nextag.com/under-counter-ice-maker/shop-html.
Under counter ice makers are specialty ice maker appliances. Some features include stainless steel doors, front exhaust fan, auto shut off, manual defrost, and ice scoop. http://www.overstock.com/Home-Garden/Under-Counter-Ice-Maker-with-Stainless-Steel-Door/3516962/product.html
Under counter ice makers are produced by companies like Polar, Apollo and Orien. They can be purchased online from Amazon, eBay, The Sports HQ and Home Depot.
Most repairmen, especially ones that work on refrigerators, will be able to help you fix your under the counter ice maker. Many handymen are also capable of fixing it at well. A specialist generally isn't required.
There's a lot of high quality models around. However, at the moment one of the top rated is KitchenAid.
Under-counter ice machines will seat underneath the counter top of a bar, and provide quick and easy access to ice. Visit http://www.ckitchen.com/commercial/ice-machines/undercounter-ice-machines.html
There are a number of places where you can purchase a under counter ice makers. I would check out sites like Amazon, Best Buy, and Sears. Costco typically has some great selections as well too.
From a shop.
Yes, some fridges allow you to buy an ice maker and install it after you purchase the fridge. Make sure that your fridge allows this.
Nextag, Walmart and Sears are a few retailers that sell a variety of under the counter ice makers. If you are lucky, sometimes they carry them at Costco as well.
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Check to see if the hose that goes from the water source (under the kitchen sink) to the ice maker isn't pinched off, or that it hasn't come disconnected.