Hi Poltava,
I think I have experience the same problem sometimes. I have the LogFile function activated, but usually solve the problem in another way:
it seems that if you write text in the briefings and save the mission immediately, sometimes that text doesn't stick, as you mention It seems that the FMB doesn't detect the edited text as a change and therefore it doesn't save it. However, by placing some random object somewhere and removing it AFTER the text is edited, it seems that the FMB is able now to detect that something has really changed and saves everything, including the new text.
I need to check this in detail, but to be sure, after editing a briefing text I always place some new object or clone an existing one, and immediately delete it before saving the mission.
EDIT: I've just tried, and it happened as you described: the new texts in briefings were ignored and reverted to the old versions. I tried what I thought it could solve the problem (locating a new object and deleting it, as described above), but it didn't work. However, I remember that somehow I was able to change the texts in briefings some weeks ago. Finally, I managed to do that, just by exiting the game just after editing and saving the mission. This time, the changes were preserved and when launching the game again, the new texts were there.
It is a bit annoying to have to close the game just to preserve the texts, so I've also tried your fix, and it works!
Thanks for telling.