A regenerating shield must not be mistaken for regenerating health. A shield usually has a seperate "bar" than health. Some shields regenerate. When your shield is almost empty, the screen usually flashes red or a beeping noise can be heard to tell you "heads up, you're gonna die".
A shield regenerates usually after a few seconds. The key to shield regeneration is to not get hit. The best way to do this is to hide behind cover.