Is there a reason that there is no running in the Fallout series?

You could run in fallout 1 (probably 2 as well, never played it)
Bethesda has confirmed running in Skyrim so it's a safe bet that it could make an appearence in future fallout titles.

Forgot about Fallout 1 (good times)

Yeah, it would be nice to see running make a return :vaultboy:

What are you talking about your, character runs all the time? I think what you mean is a sprint button...

Cuz then you'll be very tired. Running at a controlled pace is more beneficial to your heart and you probably get further too without stopping.