Operating system: Windows 10 Home 64 Bit
Graphics card: NVidia Geforce GTX 1050
When running the attached .blend file the custom property 'CustomProperty' of object 'Cube'
is always zero during render, but it is animated to go from 0.0 to 1.0 with keyframes.
With a pre frame change handler I print out the value (and change the cube material according to it),
and during render the value is always the last one dependeing on the frame currently selected in the scene.
Exact steps for others to reproduce the error
Based on the default startup or an attached .blend file (as simple as possible).
Load the attached .blend file
Make sure the script is executed at least once
open the system console
play animation to make sure the custom property of Cube is updated (Cube also changes color according to property).
Press Ctrl+F12 to render animation
Verify in the system console that custom property is not updated and sticks to last selected frame value.