I have been able to use PreCheck on two occasions when flying as a non-elite. I assume it is because I put my Trusted Traveler PassID into all my frequent flyer accounts for any all the airlines, and that has made me PreCheck eligible.

I think this is also what you want to accomplish. Some potential problems:

1) Make sure the name in your Secure Flight section of your profile exactly matches your PassID name (this is the name on your GE/NUXUS/SENTRI card). Note that for some online accounts, the Secure Flight info section is not the same as your account name and may need to be entered in a different section.

2) Pointed out by Ari to be incorrect/misinformed/untrue.

3) Make sure that there are no international legs on the itinerary

4) Make sure the airline participates in PreCheck, at that airport, at that terminal, at that security checkpoint.

That is all I can think of. #1 screws up a lot of people.