My Ubuntu-run laptop enters coma every time it goes to sleep after a period of inactivity. How do I determine the cause?

Lately my laptop, running Ubuntu 24.04 LTS, started behaving strangely upon entering sleep after a period of inactivity (or after I manually put it to sleep). It refuses to go back online. When I press keyboard buttons or the power button, normally it should go out of the sleeping state, and that's what it had been doing until recently. Now it simply continues to have black screen and doesn't react to pressing any buttons, including pressing the power button briefly, until I turn it off and back on. In all other aspects it appears to work fine. What steps do I perform to diagnose the problem?

Question by Daigaku no Baku on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.