I won't even use Singer needles at all even in my Singer machines. They haven't been any good for years. They're a lot of times a hair thinner than other needles, that's probably why they're falling out of your machine. I use Organ needles that I buy in bulk, or Schmetz if I'm in a pinch. BTW, That "Universal" label on them means the point style, not that they're universally for any machine. It means they're not quite sharp but not quite ball point either so in my eyes that makes them universally good for nothing.
Cari