My Pace RC200 is like this, the bottom head set cup drops straight out. It does it with three different headsets.
As there are no cracks and no witness marks to anything untoward I can only assume that the frame has streached as a result of having headsets swapped too often or a oversized (think poor tolerance, not Tioga Avenger
) headset cup being fitted. The tolerance involved is miniscule, a single wrap of PFTE tape makes the cup too big to fit, no tape and it is too loose. I just put some thick grease on the cup to A: hold the cup in while I assembled the bike. B: to help the cup sit evenly in the frame when all is done up, kind of like a floating bearing surface on a roller bearing headset.
I may be wrong but I am a sturdy chap and there has been no sign of any further problem since. My headset does up fine and there is no play.
Somerset, like 'Heartbeat' with newer cars!
Retro MTB: 1992 Cannondale 3.0 Deore XT M730. 1992 Marin Pine Mountain Deore DX M650.
Retro road: 1992 Eddy Merckx Corsa Extra Telekom Shimano 600 STI. 1993 Dyna Tech Ti.
Modern: 2006 Wilier scandium Ultegra 6600. 2014 Wilier GTR Ultegra 6800.