On tallships we paint
Barge Cement over all of the stitching to prevent chafe and sun degradation. Using a machine, I'd leave the existing thread in place (even degraded, it's offering some grip) and run a row of new stitches along, offset by a millimeter or so, then smear cement over it all. If you're really concerned about weakness, get some five or six ounce dacron and cut it into 1" or 2" strips (or buy a roll). Lay this over the old stitches and put your new stitches through it; I'd cement that strip in place, but it isn't necessary. It'll sure be stronger though - and once cured (about ten minutes), the barge cement won't leave a residue on your needle. It'll need thinned a bit as it's quite viscous; get it to a thick varnish
or room temp honey viscosity, then paint
You can see the cement on all of the seams of these sails
; it's works fabulously. These sails
are manhandled frequently and the stitches never give way because they're protected by the barge cement:
In a pinch, barge cement can be used to glue a patch on without stitches and it'll hold like crazy. I did this to a gaff's main after it was split from leech to luff mid-mast after a student watch officer accidentally gybed; 12" wide dacron patch glued on without unbending the sail, all in 45mins and 30kts...