That’s one of the few panelscreenshots were really everything seems to be correctly set up 
It makes no sense that while the speed seems to be sufficient, the AP doesn’t follow it’s own FD commands and speed and vertical speed increase.
1.You might be picking up ice. MSFS only simulates severe icing which occurs very rapidly.
Switch to the external view and check if your A320 is covered in ice.
If that’s the case, turn on wing and engine anti-ice, switch to selected speed and increase speed to 250kts. (Once the ice is gone you can switch to managed speed again).
2.Unlikely, but you should check if the flight model is (still) set to MODERN.
3.What is the stab trim setting when this happens and what’s the CG?
4.Since the framerate of the FBW A320 is even a tad better than the default A320s (at least on my PC), suggest to use their version. Highly recommended.
Especially since it’s obvious that you know how to operate an A320.