It is not clear to me which stay is falling out and when. You mention "during stepping" and also "in a heavy wind". If the former, my 23 lacks these baby stays (as a factory install at least), so can't add to the other comments. If the actual lower shroud is falling out as you raise the mast, use the plugs as mentioned or try tape around the mast at the point where the shroud fitting enters the mast (probably T-ball fittings?). Just cut a slit in the sail track so the tape does not block the mainsail slugs or bolt rope. I was able to fit a stainless bolt through the mast, through the t-ball fittings, above where the shroud fittings sit in the slot, installed after the fittings are in. This keeps the t-balls from sliding up as I raise the mast; make sure you cut the bolt (if needed) so it does not extend much past the nut (I used a lock nut with the nylon insert).
If instead (or in addition to), the lower shroud came out under sail I think it must be too loose, which may have been caused by the new mast - is the shroud length actually correct for that mast? I tighten mine by hand (no gauge) and I can pull the wire maybe an inch or a bit less when tight. If your shrouds (either one) seem loose on the lee side when under a good breeze I suspect they are not tight enough. If the turnbuckle is all the way in, perhaps the shroud(s) are too long for the new mast.
