I had a Singer 237 do that too. Just was madding. I cleaned and oiled and it still skipped. Finally I realized the drop feed lever was only partially working. I oiled and cleaned and re-oiled and finally got it loose and guess what, no more skipped stitches.
I had another machine that someone had put a thick white grease on the bullet that is supposed to slide lowering the feed dogs, and the grease had turned to white solid not letting anything move. Finally scrapped and dissolved it and then no more skips.
Ethel