I’m am getting a “spinner” when I click Caffeinate, so the app is hanging, right?
No. The spinner is simply indicating that CaffeinateMe is active, which means it’s preventing sleep. It doesn’t mean that content is loading, etc.
Even when CaffeinateMe is active, my screen goes dark and my computer is falling asleep! Why is it not working?
CaffeinateMe is actually working very reliably. Likely what’s happening is simply that your computer is behaving like the Energy preference panel indicates, i.e. your display is turned off after some time. However, this does not mean your computer is actually asleep.
Fortunately, you can control in CaffeinateMe whether you’d like to keep the display active while the app is active and preventing sleep: