"One day there will be a day that I will not be able to run or walk, but that day is not today. that's why I run."
It's correct, but it's too wordy and a little too formal. So while correct and understandable, native speakers usually wouldn't say this.
A more natural version is:
"There'll be a day I won't be able run or walk, but I'm not there yet. That's why I run."