transporting point-level animation

I guess this is a beginners problem. I took two objects out of a complex model for a test; pasted them in a new file and worked out a point-level animation for one of them over frame 0-25.
I then copied the two back into the original file (with "animation" tool on); they appear on frame 0 to 25 in the timeline; both visible in the viewports.

But . . . the moment I move the cursor to frame 1, the animated object disappears from the viewports and I can't find a way to get it back in view. The non-animated part works fine.

Of course I can do the (pretty complex) point-animation again in the original model, but it took me a lot of time. I suppose there must be a way to get it right.