See, that is interesting to me, and the very first time I heard that it's not guaranteed. That would make sense and explain things.
But why don't the many AA agents we speak to know about this? They ALWAYS say "Well, I see your TSA number associated with this reservation, so it SHOULD HAVE printed on the pass"

Also, in my experience the randomness factor doesn't make it "hit or miss." It means not getting Precheck on my boarding pass once out of several dozen eligible flights, at worst.

I think that OP has simply misheard a lot of things. There is no such thing as a TSA number. He has a Known Traveler Number he obtained through the TSA Pre-Check program.

The most likely reason for OP's problems is that there is a minor mismatch between the name underlying his KTN and the name under which he books his tickets. It can be as simple as an extra space, punctuation mark or a middle initial.

Make sure that you book under the name on your KTN and that any FFP profiles which prefill your tickets are corrected.

Name mismatch was my first thought, too, but that should have prevented Precheck from displaying when the checkin agent reprinted the BP as well, right?

Yes. Personally, I think the randomness factor just hit you hard and you will be fine going forward.

It's possible that the agent corrected the Secure Flight data before reprinting the boarding pass, resulting in Pre✓ coming out.

Hit the OP, that is. Thus far, the Fickle Finger of Fate has missed me; unless you count the time irrops led to my being rebooked on UA and not getting Pre on their BP.

Yes, I have a KTN issued by TSA, but generally just call it my TSA number.

I'm looking into the name mismatch thing now, which is very possible. I have three upcoming flights in MY TRIPS. Two of them show my first and last names. The third, booked via my travel company, shows First Middle and Last.
So I click on my name under edit passenger information, and my KTN is blank under the agency reservation, but it's there for my other 2. I add it into the blank one and save it. Go back, and not there. Definitely not letting me assign my KTN to this reservation, even though it's already assigned to my two other flights. A phone call is in my future...

Unless I'm mistaken, the randomness issue will arise if you are just counting on the airline flagging long-known customers. If you have a Trusted Traveler number in your individual record, on the other hand, I'm not aware of any randomness at all. The government rightly wants to focus its resources, so if someone who has been finger printed and interviewed and had background checks, etc. from TSA or Global Entry, I'm not aware of any instance wherer TSA Pre won't be granted. Separately, there are random checks of TSA Pre passengers such that if a random beep sounds, they check luggage, etc.

I've been SSSS'd once, in which case PreCheck naturally didn't appear on my BP.

Your not promised Pre-check with known traveler number. I have been SSSS on one leg of a two leg flight with pre-check on the 2nd leg where I can transfer airside to my connection and have no need for security.

Same thing, except for me, I was past security already, and got SSSS reprinted on my pass, so at boarding, wasn't allowed to board. Guess who missed that flight to walk back (despite being in the sterile zone) and get the full scrub down.

Always worth a shot to have the agent remove your KTN, then re-apply it and print the pass.

It is possible to reprint a boarding pass at home and "retrieve" the missing pre check notification. Last year I was traveling on WN from SAN to SJC. As it was an in and out on the same day for a 2hr meeting, I decided to forgo the SAN-PHX-SJC routing on AA and opted for the direct WN service. I had booked through my corporate travel agent and I hadn't updated my traveler profile for WN, so the KTN was never sent to WN. I only noticed when I checked in at T-24 that PRE was missing. I called WN customer service and had them add my KTN to the PNR. The agent advised me to reprint the BP and it did indeed have PRE showing on it.

In addition to verifying your KTN number is correct.... Be sure your DOB, Sex and name match the information on your application. It's very important that they match perfectly.

Very interesting. Exactly what we tried with AA, and the phone agents could NOT do that. They advised, "you're already checked in and BP was issued, so nothing we can do."

P.S..... Why does AA love sending us to Phoenix even when traveling within CA, lol?
I have to give Southwest a try like you.