A good sling that is cared for decently should last just fine for as long as you need it. An 80 or 100 year old year old sling on the other hand, well, try to be nice to it.
I found a neat one on ebay a few years ago - two halves of a 1905/1908 Rock Island Arsenal leather sling, each half having a different date. It was in average shape but one side needed a little stitching so I got it for about 27 bucks (I always loved those honkin' Rock Island Arsenal keepers with the hand-bevelled edge - no one else has them quite like that);
But what was really neat was that it had some nice Cavalry markings on it.
Not wanting to deal with trying to preserve it and not 'in' to the early '03s (or whatever this might have been used on), I traded it to a guy that I knew would like it. Now, not knowing what it was actually worth, I just gave it to him and told him what I paid and said 'surprise me' with something from your stash of 'trading fodder' (every serious guy has stuff that he got for a deal so he can trade for what he wants ...). Well, nice guy that he is, he gave me more stuff then I ever imagined - apparently he was VERY excited to see this little sling! I started feeling bad cause I paid so little. I still think I owe him something in return - I'll get him back, don't you worry.
How often do deals turn out like that ...