I have a NEXUS card which gives me a known traveller number. Usually
I get precheck on my boarding pass, but sometimes I don't, and I can't
figure out what the difference is. TSA vaguely claims random
something but I don't believe them.

On a recent trip, I intended to fly ITH-EWR-FLL / DFW-EWR-ITH, with a
FLL-DAL leg on another airline. I got precheck on the first and
FLL-DAL but not on the last one, which was a surprise since I never
precheck on one leg of a trip but not another. I suspect the problem
was that due to airline screwups, we drove to EWR so I called them to
delete ITH-EWR which they did (their problem, plane was two hours late
on a 50 minute trip.) So when I checked in for the return, I had to
call them to do something to the ticket to allow me to check in. That
probably made it look like a last minute purchase. But it was still a
pain.

Bonus mystery, my wife flew ITH-EWR-FLL / FLL-EWR-(ITH), same deal, got
precheck on everything even though she never signed up for anything.