It's the former, which is the only screw I see. I made a mistake in saying I had a DX-390; I have a DX-392, the bulky one with the cassette recorder. I see the 390 is a completely different design, looking more like my Grundig G3, which works fine and has had no antenna problems.
The DX-390 is not a completely different design from the 392 -- the radio circuitry has small differences, and -- of course -- the 392 has the cassette recorder included. The size of the cabinets and overall operation (aside from the cassette deck) is the same.
I don't know of a fix for a loose screw that secures the whip to the post aside from a new, longer screw with a nut on the other end...Another 'fix' would be inserting a very small, fine washer inside the post, next to the whip itself -- it would tighten the connection that way.
I have never had that problem with my 390. Maybe I've been lucky. I've only used the whip for FM, and not all that often.
I have had the problem of the screw holding the entire whip assembly to the case loosening on one of my radios, I think it happened once but can't remember which radio it was, and it hasn't happened to me in over 10-15 years.