It sounds like there is a short somewhere. Have you recently replaced these batteries? Some of the new ones have the top of the casing sticking up beside the top (positive pole) and some remotes are not made to take them, causing a short. If it still happens with new batteries it could also be a short in the circuit itself, in which case the remote should be repaired before the components burn out completely.
Some remotes get dust inside them. When that becomes moist through people holding the remote when watching the dust may short.
Some thoughts to consider.