How long should your heart rate stay elevated after workout?

It depends upon what "elevated" means as well as your level of conditioning. It is best to check with your physician in advance. As a rule, three minutes after your fitness exercises ends, you should be lower than 50% of your predicted maximum heart rate. Therefore, figure out your predicted maximum heart rate in advance (or just ask your physician) and check your pulse three minutes after the end of your training. If it is too high, your are training too strenuously, so reduce the intensity of your training and build up more slower to a greater degree of fitness.