When serving cold brew or nitro coffee on draft you want to make sure to only use pure nitrogen. If you use CO2 (which is used for carbonated beverages like sparkling water, beer, or soda) it will bitter the coffee, and give a sticky mouthfeel after just a short period of time (usually within 24 hours).
Even when using a beer gas blend (which is usually about 25% CO2 and 75% Nitrogen) this small amount of CO2 will also ruin the mouthfeel and flavor of the cold brew in a matter of 24 or so hours. Beer gas blends are used when serving stouts on draft, like a Guinness because the beer needs a small amount of carbonation. Although nitro coffee is served out of the same stout faucuet or as a Guinness, just make sure you use only pure nitrogen when serving on draft.
Nitrogen is a gas that will not effect the flavor of your beverage.
If you are using pure nitrogen already, then using equipment that is not properly cleaned could be the issue. If not cleaned with proper cold brew equipment cleaner, and followed up by a sanitizer, you likely have left over bacteria or mold spores in your equipment that can begin to change flavors and potentially be dangerous.
Always make sure you are cleaning and sanitizing all of your equipment that comes in contact with your cold brew coffee; cold brew coffee maker, kegs, draft equipment (draft lines, faucets), etc., on a regular basis.