Classic symptom of a bad connection at the battery. Especially if your dome lights don't dim while it's doing this. The connection could look good, but not be good enough.
If you grab the cables near the posts and try moving them around by hand, they shouldn't move at all. Even then, I'd take them off, clean the post, and the inside of the connector that sits on the post with a wire brush or something.
The jump start fires enough power through the issue most of the time, or slightly impacts the connection enough to appear to be fixed.
I cleaned the mess off of a customers battery once, and it got towed back in. Cleaned them again, got towed back in. Third time I got the wire brush on it. I knew what the issue was each time by measuring the voltage between the battery post, and the connector itself. There should be 0v there, and very very little during cranking.