Try a different package of needles. It might be the manufacture.
I had a bad Schmetz needle. It bent but didn't break and made noise when it hit bottom. I took the machine in and the repair man showed me that the needle was too long (1/32" +/-). I saved the needle for future
comparison.

I've never experienced that particular issue, but I would agree it could be the needle....OR... the mechanism/parts that hold the needle in place inside the machine could have worn resulting in the fall out. ... but I'm sure you thought of that. Let's us know if a different pack of needles solves the problem.

Thanks for the suggestions. The replacement Singer was from a new package, then tried the Schmetz. Just had the machine serviced, he said it was in great shape. I REALLY tightened it last night and so far so good.

Try removing the screw completely that holds the needle in and cleaning the 'slot' that the needle goes into and the end of the screw. a teeny bit of lint or dust would make the needle clamp not hold the needle tight. When you really tightened it, you may have compressed the lint. You can really damage your shuttle and hook if the needle comes out while sewing, but you already knew that. :)