The sequencer doesn’t render scene strips in an animation if the display method is set to Rendered.
It previews scene strips and can render an image in this mode, but not animation.
This happens even in a default project with a fully reinstalled app. I had this problem initially, then it disappeared and I was able to render an animation with scene strips using compositioning, but now it has returned again.
Welcome 
…
Somethign like this… (only in 3.6.15) and it does not work in 4.2.1 ??
SequenceTest.blend (118.5 KB)
Hei!
The result is the same: the scene strip is rendered in the image and not in the animation.
Tested on versions 4.2.1, 4.2 and 4.1 on two computers. Sometimes scene strips may be rendered during some frames in the animation.
The animation will be rendered in single images, but i may not understand this sentence :
After the scene is rendered and moving the “frame cursor” in the sequencer also the images in the preview changes accordingly (again in 3.6)…
…oh you mean this ?? The scene as to be rendered before it is viewable… that’s also the reason why i thought you first sentecne is a bit strange:
In the Video Sequenver → Preview you can’t set it to rendered (…solid, wireframe) like in the 3D View… and of course there is nothing to show/see if not rendered before ( *Render → Render Animation * or by adding a prerendered clip)…
The animation using the Material preview shading mode: https://imgur.com/a/SDuG8JY
The animation using the Rendered shading mode:
https://imgur.com/a/ZD8ZI9M
But you can and it affects the final result:
I’ll try to clarify: in the preview everything is shown perfectly with any shading method, but when trying to Video Sequencer → View → Sequence Render Animation, scene strips are ignored only in the Rendered mode. It’s still possible to Video Sequencer → View → Sequence Render Image in this mode (scene strips will be shown), but the animation renders scene strips in all except this mode.
But only the Rendered mode allows compositing, and once I was able to render animation in this mode.
Oh, I got it!
I didn’t try to Render → Render Animation in the scene where the sequence is. I thought that it’s possible to render the sequence animation using only Video Sequencer → View → Sequence Render Animation. That was the issue! 
