Built-in Save Points are placed before chapter select is updated

[Exp HP]

Right before a class trial begins, the following occurs, in this order.

1. The game asks you if you want to save. If you do, the save is named "Chapter 3 Save Point".
2. Chapter 3 class trial gets unlocked in chapter select.
3. The prep screen appears.

What this means is that the class trial is not unlocked in the "Chapter 3 Save Point" save file. If you load this save and use chapter select, then when you are ready to return to where you left off you will have to replay Deadly Life. To get around this, you need to save manually from the Monopad on the prep screen (or after), so that the save file is called "Chapter 3 Class Trial (Preparation)".

IIRC, Danganronpa 1 was like this as well with the "Chapter X END" save points (to correctly update Chapter Select you had to make a manual save after the save prompt). However, in that game it wasn't a big deal compared to the much bigger issue that you only unlocked the previous chapter.