Unannounced limited-time special events are sort of irritating and not a very good decision from a design standpoint. To accomplish the same purpose (special event fights that can only be run a limited number of times for exceptional loot), a better design paradigm would be handling these similar to Raid bosses:
1. Opening up the time window to the entire day
2. Restricting the number of times the special event can be run (e.g., 3x per day, or 1x per X rank attained)
3. Offering items that increase this limit (instead of restoring AP). This could scale with rank or AP or whatever if you wanted to retain that scaling factor.

That would make this more casual-friendly, which these games are SUPPOSED to be. Unless of course the purpose is to prod disadvantaged players to buy elixirs. This is particularly unfair because the game was designed to be played in a single timezone (Japan), whereas the English version is played in many different timezones and any given several hour range will tend to favor certain timezones and exclude others.