Whips and floggers get worn out sometimes.
Some pieces can be fixed, others can't.
Don't get sentimental about gear. If one of your favorite toys has had a good run--many beating sessions, many years of fun--and some part of it has finally snapped, let it go. If you can't repair it, then buy something new. There are many BDSM toy shoppes and plenty of custom craftspeople. They're happy to provide you with new gear when the time has come.
Every once in a while, I get a little bit sad if a favorite toy breaks during a session. I think that all of you S&M kinksters out there probably understand what I mean--sort of, kind of. There are whips--and canes and floggers and crops--that have unique designs, colors, textures and you think to yourself "Gosh, I hope that I have this whip forever!". Or maybe you got it at some special event. You get attached to it but one day, you'll hear a "crack!", "pop!", or "crunch!" and a part of it may go flying across the dungeon in mid-scene. And that's just awful.
It's funny to think that you can become sentimental about a piece of equipment that you use to hit people but, hey, some pieces of gear are really, really great. It sucks having to replace things but it's better to call the situation as is. Simply toss out that dead whip--no matter how cool it is, no matter how many happy memories are attached to it--and just go get a new one. And, no, don't let that broken whip sit on your shelf for aesthetic reasons--throw it away. Just allowing it to sit there is too damn depressing.