Check to see how little you need to turn your key to shut off the engine. Can you make it quit by wiggling the key? Many times a flaky ignition switch can kill the engine with just a tiny turn.

 

ok, i did the wiggle the key thing and it didnt turn off. i had to turn the key all the way to turn the car off. it does have keyless entry on the car its a remote that has honda on it so i know there is a security system on it but i think its stock cuz nothing has been to to the car, its all pretty much stock. would it make a difference if there is no radio in the car?

 

I haven't had a factory security system screw up like that, so I don't know...? (but I'm no expert on that stuff)

Check (to rule out) for dirty/corroded/loose battery cables, especially the opposite end not at the battery. Don't forget to check where the actual cable is crimped into the end connectors.