How to remove the drill bit from the hammer drill

Assuming the drill you have is working properly, you may have dull or worn bits. A masonry bit does not last long, especially in concrete or brick. Cheap bits are no bargain. Start with a new bit, when the speed of boring slows to about half or less, time for a new bit.

Have you tried using a Screw Extractor bit?

They are made for this purpose. You basically put it into your drill and when the drill slowly turns in reverse, the bit bites into the screw and tries to unscrew it simultaneously.