Is it too late to return the jacket? That's an awful important piece to just fall off so soon. Usually it takes a lot of wear to make that thing come off and typically it would tear away rather than fall off.
Do you have any old jackets that you could try to take the pin off for a replacement? Do you know anyone handy with tools that could fashion a new pin with crimping tools?
I have a jacket with snaps very close to the zipper also. But, if I had to replace the zipper I think I could by working slowly, carefully trimming the zipper edge around each snap and reinforcing the stitches so it wouldn't fray. Sorry, probably not a lot of help, but it's all I can think of.

Yes, I'm afraid it is too late to return and bought it in the US (I live in the UK)...anyway, I did try to fashion a new pin (I have jewellery tools) but it just wouldn't work. It didn't fit right and so the zipper teeth wouldn't engage properly. I think I'll take it to one other tailor who's been recommended. If he doesn't want to mess around with the snaps, then I will try to do it myself. Maybe I can find a similar zipper and sew the bottom bits onto the old one. Or just bite the bullet and try to sew in a whole new one myself. Thanks so very much for taking the time to write and make helpful suggestions. Much appreciated.

NHow

I had the pin part "replaced" at a tailor. Do you mean the little slide you insert into the opposite side of the zipper before you zip up. The seamstress/tailor was able to replace just that little thing. Didn't have to replace zipper, but maybe there is more to your situation. Check around for another seamstress.

None of the tailors I asked would touch it. So I bought a zipper that was the same size and did it myself. So far it works fine but don't know for how long.

I cut the insertion pin off the new zipper. Then I removed the old one (including the bottom bit of zipper tape). I glued and hand sewed the new bit of zipper tape with the new pin into the seam of the jacket, lining it up as closely as possible with the bottom of the zipper. Then I hand sewed the top bit of the new zipper tape to the bottom part of the old tape fairly close to the zipper teeth (but not so close as to jam the zipper). Finally, I used some jewellers glue to stick the insertion pin to the bottom of the zipper teeth. I let it all dry overnight then tried it. It was a bit reluctant at first but then it worked. It's worked ever since.