Hi. TCM exec here. Well, not quite exec, but senior-level. Happy to bring some light to the speculation.
There seems to be two different issues being discussed here.
1. the change in programming to pay tribute to a star.
2. the memorial montage (that's about 90 seconds long) that we produce for the dearly departed.
When a star passes away, especially a big star, it is not easy or quick to change the programming in order to properly eulogize them. It's akin to turning around an aircraft carrier. The changes have to be communicated to affiliates. Licenses need to be buttoned up. New intros have to be shot with the hosts (all of whom would need to be flown in to Atlanta). Intros would then need to be edited, sent through a sound mix and posted for the Broadcast Operations Center to air. We also use the memorial montage (the :90 second thing) to promote for our viewers the programming lineup change, so there needs to be time for that to occur. And PR would need the time to raise awareness of the the changes in case a news outlet would want to cover the memorial tribute lineup in honor of Dearly Departed Big Star. And sometimes the programmer chooses to wait until much later than a month or so (such as the aforementioned Burt Reynolds salute we did in December) because certain titles would not be available to us until later. Now, that's just the programming for the tribute. What would have to move to accommodate it would need to be carefully considered too. If TCM has a license to air a Fox film, for example, and that license expires on a certain date, then we'd need to consider if it would be possible to move the airing of that film to another day. And it wouldn't just be that one film; we'd have to consider all the other films that were thematically grouped with that one Fox film too. Programming the channel is tricky. It's not like alphabetizing your DVD collection. So, the longer lead time we have to air the memorial, the better. Sometimes it works out to get it on the air quickly, usually it doesn't.
Insofar as the memorial montages are concerned, yes, we have many of them in the can prepped to go. Not always, but usually. That's why you see them on the air much quicker than the programming changes.