During the time I was active in competitive running I also experienced a reduction in heart rate a day or two after a race. This would generally decline from around 46 to around 40. I am not sure why this is and I always thought it might be related to less resistance for blood flow through expanded arteries? However, I never felt oxygen deprived and this may indicate something more serious. In addition to the lower rate, following a race I would become dizzy when standing. Sometimes this was so bad I would need to hold on to something for a few seconds to keep from fainting.
I agree, a HR below 40 is in the problem range, regardless of you physical condition. I think it is common for people who run at you level have resting HR in the 50s, but not below 40.
You didn't mention what your HR had been in the past, or when you have not had an "extreme" workout. What is you base-line or normal resting HR?
Hey, I have always heard that athletes have lower heart rates but if you are feeling oxygen deprived i would definately talk with a cardiologist. Getting down in the 30's is a little low. It never hurts to establish care with a cardiologist so you have a baseline anyways. Also, if you have low iron you should take an iron supplement.