Shuts off after 2 second

This has been a great little car. However, as of a couple weeks ago it occasionally starts normally and after approximately 2 seconds the engine will turn off. It doesn�t matter if I rev the engine or if the car is cold or hot � it will turn off after two seconds.

It will usually repeat this behavior, sometimes for only a couple minutes and other times I give up and try it again later and it will keep running. After the first shut-down, the engine becomes harder to start and once started will run more roughly until it shuts down again or is given a lot of gas. The condition is occasional and feels random to me and it does not change if I rev the engine while starting it. It feels like someone just turned off the car. I don�t think it has anything to do with the ignition switch since I return the key to �On� right after starting and then 1.5 seconds later the car turns off. I also don�t think it is the security/transponder cutting the engine because the green security dashboard light does not illuminate and in the past when the security has engaged, it stops the car from starting all together. The car does have an after-market remote start that has been working fine for the last two years and a decent battery (although I�ll probably replace it before this winter). I also don�t think it�s a fuel issue since I can be flooring the gas pedal and the car will still shut down.

I�ve checked the fuses, replaced the ignition coils (they were shorting out and causing hesitation), and cleaned out the air intake but I have no idea what else to try. The Check Engine Light has been on since I got the car and the error code is always low compression in cylinder 3, but I have had it checked multiple times and the compression is good.

Any help would be appreciated - thanks!