A stuck fermentation occurs in winemaking when the yeast becomes dormant before the fermentation has completed, fermentation has stopped before all the available sugar in the wine has been converted in to alcohol and CO2. If the winemaker was to give up on the wine at this point, it would taste semi-sweet and possibly pretty bad. That would be a shame, and what's more, a waste of good grape juice and wine!
Unlike an 'arrested fermentation' where the winemaker intentionally stops fermentation (such as in the production of fortified wines, like Port; where spirit is added to the fermenting juice to suffocate/ arrest the yeast), a stuck fermentation is an unintentional and unwanted occurrence that can lead to the wine being spoiled by bacteria and oxidation.

 

There are several potential causes of a stuck fermentation; the most common are excessive temperatures killing off the yeast or a 'must' deficient in the nitrogen food source needed for the yeast to thrive. Plus if the sugar concentration level of the 'must' becomes too high at any given point, either at the beginning or during the fermentation, it starts to have an inhibiting effect on the yeast's ability to produce alcohol.
Once the fermentation is stuck, it is very difficult to restart due to a chemical compound released by the dying yeast cells that inhibit the future growth of new yeast cells into the batch.
There are various techniques a winemaker can use to minimize the chances of a stuck fermentation happening, such as adding nitrogen to the 'must' in the form diammonium phosphate or using cultured yeast strains with a high temperature and alcohol tolerance, coupled by diligent control of the fermentation temperature. These steps that winemakers may take to prevent a stuck fermentation will each have their own subtle or dramatic affect on the resulting aromas, flavours and quality of the wine produced.
Luckily, stuck fermentations don't occur very often - but when they do, it is important to make the right corrections straight away and get the fermentation going again.