Hi StephenMansfield,
Thank you for reaching out to Microsoft Community.
Can you please check what is the current Driver versions of the Graphics driver of both device then share it with us here. Go to Device Manager, expand Display adapter. Double-click Intel HD Graphics then go to the Driver tab where you'll find the Driver version.
For now, please do these steps on the Surface Pro 4 while the monitor is connected:
1: Clear Display cache
Go to this page and refer to Solution 5 : Troubleshoot connecting Surface to a second monitor.
2: Run Surface Diagnostic Toolkit and check Windows Update
3: Update drivers and firmware
Check what is the current OS Build of your Windows version by going to Settings > System > About.
Go to Download driver and firmware for Surface, choose Surface Pro 4 then click Download on the next page.
Choose the .msi file that matches your current OS Build and click Next.
After downloading, run and install the .msi then Restart.
If this answer your question, we highly encourage you to inform our Community by clicking on Yes or marking my post as an answer. This will help other members who may have the same issue as you. Otherwise, don't hesitate to update us so we can further assist you.
Kind Regards,
Marrion Y.