DeusXM,
Amazing observation. I rarely know what my heart rate is. I generally assume that it is still beating.
If you are a runner it might not be unusual for your resting heart rate to be that low. You might want to mention it to your doctor at the next visit. The racing/falling thing seems like a potential problem to me.
I recall reading something about that in Men's Health last July in their special heart issue. If you can find it you might want to read the story on Jim Fix. He was the father of the modern running movement. He dropped dead after run. If I am not mistaken, the article mentioned that the rapidly descending heart rate was a contributing factor.
Although you are probably fine, it wouldn't hurt to get checked.
Travis