I have had many panic attacks in the past couple of years. They don't come as often now, but it still happens just like everyone else and it is perfectly normal to have this emotion sometimes.
Anyway, I do recall having "panic attacks" but my heart did not race. This happens more and more often nowadays.
I'm not a doctor, but I believe that your heart may not be racing sometimes because you are getting better. Its possible that your body recognizes that you are just anxious and there is no threat, so the adrenaline doesn't kick in. I could be wrong, but with my experience, this is a sign of your self improvement excercise working. And you are getting better at managing your anxiety.