There was a post I read (not sure if it was on here or on the 'sew diaper' forum...but there was a mom that used the following technique to 'save' some fuzzi bunz that had lost their leg elasticity (I have some that need to be fixed as well, just haven't done it yet...

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She 'felt' where the leg elastic attached at the upper and lower ends of the diaper leg area. She made two small slits in the fleece right near where the elastic attached. Then she attached a small safety pin to one end of 1/4 inch elastic and 'threaded' it into the elastic channel. Once she had it out the other end, she stitched it down. Then she just pulled it until it was about the right 'tightness' and stitched the other end down and cut off the excess. She 'slip stitched' the opening closed and they worked great!
I noticed that those wraps have gussets, and not regular 'leg channels'. So if you think you can get an opening big enough to allow you to re thread a new, thin piece of elastic, I would think it would work. Since it's a wrap, the spot where you 'slipstitch' shouldn't actually come into contact with baby's skin and cause any irritations.
Otherwise, it'd be a pain to rip the seams, create a new gusset elastic, and re sew...doable, but a PITA..

If it has elastic in the back/front tummy areas, the 'leg channel' technique should work easier.
Good luck!