OSHA no longer allows you to repair extension cords, I can tell you first hand, I was fined for it a couple years back, I had an "aftermarket" repairable end on 2 extension cords, and got a $500 fine for it... The cords were in great shape but it was cheaper back then to buy a 100 footer and then cut it in half, put a new end on each half and call it a day, the longer cords were nice and thick... Well learned tha hard way osha dont approve that practice..
Now, if you have a damaged cord and fix it properly there is NO reason it is unsafe in my opinion. I still fixed them after I got fined, except I kept them for my own personal use.
If there was an abrasion in the middle of a cable, I would dissect it, and find the damage, cut the damaged wire {tin the ends of it} and repair it with a shrink coupling, then I would cover it in liquid rubber, then the final step was to slip 2 layers of shrink tubing over it all, I would do 1 at 6"s and 1 at 12"s, each time sealing the ends with more liquid rubber...
I have 5 or 6 of them in my garage, I am confident enough to use them in the rain...