My first thought was I was born with ten of them.
I've never heard of a hair based brush that will never lose a bristle. Not Purdy, not even a Kolinsky Series 7. If it's got hairs, there's a likelihood it will lose one eventually (though acid brushes are by far the worst here). That being said, I see that there are cleanroom rated brushes with nylon bristles that are bonded with high temperature (autoclavable) adhesive. If you're treating a large area, perhaps a silicone brush (like a bbq mop, baster, or glue brush) would work. It's possible to tear off a silicone whisker, but they don't just fall out, and they would be large enough to be easily seen.