Blender Version
Broken: version: 2.80 (sub 58), branch: blender2.7, commit date: 2019-04-21 20:30, hash: rB797539e76ccf
The "Influence" control that shows in the N-menu of the NLA editor when having a NLA Strip selected (under "Evaluation") can be animated and it works just fine.
But the UI portion of it (the slider in the menu) does not update at all when playing the animation, it just stays at the value it last had.
This might also be the case for the other sliders in this category - I haven't tested!
Reproduce: