Hey jlpate,
Thank you for using the Apple Support Communities! We understand your iMac appears to shut down when left idle, instead of going into a Sleep mode. Let's help.
Does the same thing happen if you manually choose to put your iMac to sleep following these suggestions: Put your Mac to sleep or wake it. Meaning, does it shut down instead of sleep when you do that?
You checked Energy preferences. Did you ensure there are no schedules set up to shut down? Schedule your Mac desktop computer to turn on or off. If you have your iMac connected to a UPS, check: Set when your Mac shuts down while using a UPS.
Do you have either of these options enabled: Set sleep and wake settings for your Mac, "Keep your Mac from going to sleep automatically: Click Power Adapter, then select “Prevent your Mac from sleeping automatically when the display is off.”
"Put hard disks to sleep: Click Battery or Power Adapter, then select “Put hard disks to sleep when possible.” If so, can you disable those and test for resolution.
Do you have any external displays or other peripherals connected to your iMac, besides a mouse and keyboard? If so, when you disconnect those does the behavior continue?
If you were able to rule out a setting as the cause of this behavior, we would suggest resetting the SMC and monitoring for improvement: How to reset the SMC of your Mac
Best regards.