1. To repro, extract the zipped unity project (AmbientOcclusionBug.zip), play the SampleScene
How I made this project:

Downloaded HDRP package, set up HDRP asset
Enabled dynamic resolution on Camera
Enabled dynamic resolution on HDRP asset
Add Volume component with Ambient Occlusion module
Added ChangeDynamicResPeriodically script to scene (every 1 second, decrease the resolution by 10% until reached minimum value, then increase res by 10% until reached maximum value)
2. I expect to see ambient occlusion on the cube to stay in the correct position (CaptureGood.png)
3. Instead, I see the ambient occlusion "falling down" towards the bottom of the frame as the resolution decreases. As the resolution increases, the ambient occlusion dark areas return to their correct position. (CaptureBad.png)

Notes:

If I disable Direct Lighting Strength on the Volume then the error does not occur, but I also don't see any ambient occlusion dark areas at all I assume because they have 0 strength.
This project is using 2019.3.0f3 and HDRP 7.1.7
I also saw this behaviour in 2019.2.13f1 with HDRP 6.9.2, which caused us to attempt an upgrade to see if this behaviour was fixed