The solution to the problem: Always use the four-step purchase method.

This issue doesn't have anything to do with the new website, as it has been an issue for at least a year.

After months and months of complaining about the same thing, I finally got an email from someone who knew what the problem was:

Your Known Traveler # will disappear from your profile if you use the two-step purchase method - the Purchase Now option - on the Trip Summary.

When you are ready to purchase a ticket, don't use this shortcut method, and click on Enter Passenger Info and through the long process.

Once I was told of this workaround, I haven't had the disappearing KT# since.