An “unforgiving minute” suggests something like “the longest minute of your life”.
“Sixty seconds’ worth of distance run” is alluding to the fact that running long distances is tough. And you force yourself to do “just one more minute” to keep on going.
So when you are facing the longest minute of your life you make yourself keep on going; the unforgiving minute is one in which you push yourself, because you know that you have to - but you also know that most likely you have to push yourself for one more minute again and again.
So what Kipling is saying is “if, when - despite things being tough - you can force yourself to keep going, even though you know the next minute might be as tough, or even tougher…”
“Sixty seconds’ worth of distance run” is alluding to the fact that running long distances is tough. And you force yourself to do “just one more minute” to keep on going.
So when you are facing the longest minute of your life you make yourself keep on going; the unforgiving minute is one in which you push yourself, because you know that you have to - but you also know that most likely you have to push yourself for one more minute again and again.
So what Kipling is saying is “if, when - despite things being tough - you can force yourself to keep going, even though you know the next minute might be as tough, or even tougher…”