Using iMac Pro (mid-2011) as 2nd monitor

Try setting the 2011 iMac to Never Sleep and let the Macbook Sleep.

see the fifth parragraph at > Use your iMac as a display - Apple Support

Learn what happens when the primary Mac goes to sleep and wakes up

The external display iMac behaves differently depending on how the primary Mac goes to sleep.

• If you put the primary Mac to sleep: After you put your Mac to sleep, the external display iMac goes dark for a few seconds and then displays the windows for its own open apps. If it doesn’t, press Command-F2 on its keyboard.
• If the primary Mac goes to sleep because it was idle: The external display iMac goes dark and stays dark. If you want the external display iMac to display the windows for its own apps, press Command-F2 on its keyboard.
• If the external display iMac doesn’t show the right desktop after it wakes up: When the primary Mac wakes up, the external display iMac displays the windows for the open apps on the primary Mac. If it doesn’t, press Command-F2 on the keyboard of the external display iMac.

I have my late 2009 and late 2006 stay in target display mode for my gaming pc and mac pro and they stay in target display mode unless i hit command F2 again, they never sleep on their own and stay as standalone monitors so it might be a certain setting you have enabled on one of them? try turning off sleep after a certain amount of time on the imac in energy preferences

I wonder if setting up Screen Sharing & using Keyboard Viewer on the Target Mac to execute CMD+f2 would work?