I have a 2002 CR-V, bought it new. Recently it has been having starting problems on and off. Sometimes it fires right up, but then next time it will take a few times to turn over. At the same time I have noticed the immobilizer system indicator flashes after the engine starts and keeps flashing until I shutdown. Could these be related?

I have made sure not to have other keys on the ring or other metal objects to confuse the immobilizer.