It may be that you have a filter set that is preventing the capture frame from showing up in the filmstrip at the bottom. Make sure that Library > Enable Filters is unchecked and then try capturing the frame again.
Next, it may be that stacks are collapsed by default. Do Photo > Stacking > Expand All Stacks. Now when you capture a frame, it should appear in a stack at the bottom, but with the stack already expanded.
Finally, if you are currently viewing a collection or smart collection that contains the video, that is, if the collection is selected as a source in the Collections panel in the left column of Library, then when you capture a frame, it won't show up at all, because LR doesn't automatically add the frame photo to the collection.
I have the same issue, it's not a that the video is in a collection or that Filters is unchecked. When you import it puts your files in a Import "bucket" that acts like a collection. If you right click on any image and select "go to folder in library" you will see the image you captured from video as expected.
When you import it puts your files in a Import "bucket" that acts like a collection.
Thanks, that's an one more thing to check. When you import, by default the current source is changed to Previous Import in the Catalog panel on the left-hand side. As you observed, with respect to stacking, Previous Import acts like a collection, and stacks are specific to the collection or folder in which the stack is created. Capture Frame creates a stack in the folder containing the video, so you can only see that stack when you set the current source to the folder or All Photographs. (One more wart caused by LR's weird stacking design.)