So I got frustrated already and made some observations for almost EVERY festival under those circumstances lol:
SE, every festival is triggered except Festival of Snow.
Solution: I had had a restaurant in Yukimatsu neighbourhood and changed its lot type from restaurant to cafe. The next week the problem went away. Only Festival of Light shown on the calendar (only for the current week, not for the upcoming ones). I guess it is a similar issue happening with CL, the restaurant keeps the festival from appearing.
CoL, Finchwick Fair is triggered.
Notes: There is a restaurant inside Finchwick neighborhood I placed a while ago. If you are first going to the restaurant, you can see the fair is triggered but the restaurant is not functionable (you cannot click on tables to request them). If you choose going to The Gnome's Arms first, then switching to the restaurant, everything is just fine. Always on the calendar.
CL, every festival is triggered.
Notes: I have been using a restaurant placed in the land of The Old Salt House for a long time; there is nothing problematic so far. The only annoying thing about CL festivals is, they cannot be seen on the calendar, they are appearing just before a day or on the time they start.
IL, every festival is triggered (the ones I did not try: Turtle Hatching and Family Fun Day - I do not have any idea about them)
Notes: I also had a restaurant placed inside O'Hanali Town, every festival do trigger and the restaurant is working fine.