Hello,
This behavior is expected when a default variation is set and Additional variation images are used.
On variable products, once the page loads, It automatically selects the default variation and replaces the main (parent) product image with the variation image/gallery. Since the video is attached to the parent product image, it gets overridden by the variation image, which is why the video no longer appears.
This is standard behavior when variation images are assigned. Currently, videos can only be attached to the main product gallery, not to individual variation galleries.
If you want the video to remain visible, you would need to avoid setting a default variation, or Avoid assigning variation images. If you disable the “Additional variations images” from Theme Settings > Shop > Variable product then it will work as you want.
Best Regards