CP88 Manual:

• Depending on the instrument status, the power may not
turn off automatically, even after the specified period of
time elapses. Always turn off the power manually when
the instrument is not in use.

I'll let Yamaha illuminate what those conditions may be.

BTW - you can see Yamaha's response to the conditions of why Montage, a different product, may not automatically turn off and see if your instrument meets any of these conditions. Then change your setup and see if now autopoweroff works.

https://www.yamahasynth.com/ask-a-question/yamaha-montage-does-not-turn-off-automatically

Thanks J and others; disconnecting the USB cable -- even though I didn't have it connected to a live computer (?! - strange) -- seemed to fix the problem. The unit now turns itself off automatically as you would expect, presumably after 30 minutes although I didn't time it. If there's a FAQ, it would be nice for Yamaha to provide this information explicitly so people don't have to jump through hoops to find it out.
Best all!

Perhaps your computer powers the port even when the machine is off. Sometimes this is something you can turn that off. This may be part of what's "hanging up" the auto power off feature.

The documentation is in the owner's manual (Page 21).

https://usa.yamaha.com/files/download/other_assets/7/1180527/cp88_cp73_en_om_d0.pdf

Auto Power Off Function
The Auto Power Off function automatically turns off this
instrument after 30 minutes of inactivity. By default, this
is set to “Disable.”

... the owner's manual (this same area) is what I quoted previously.

I'm finding all of this information by loading the owner's manual PDF and using the search feature on a single manual.

Hello,

It's important to know if you have anything connected or if you are in an edit mode.

If you have CP connected via USB to a computer CP (smartly) ignores auto power off. Even if you don't have the DAW up and you just remain connected it's disabled, and possibly even if it's connected to a computer that is off. It may still register "connected" internally.

Also, auto power off is interrupted on CP if are in an edit screen like SETTINGS or MENU. I'm reasonably certain it only works when the instrument is in an active Live Set (not in an edit state), is not connected to a computer or iOS device and the auto power off is engaged.