Hi Roger,
Normally the cabin table should remain secure, so I'm wondering if moisture got into the existing screw holes, perhaps rotting the wood in that area. If you determine that it is solid and dry, I would clean out/drill the existing holes and enlarge them under the pedestal flange where that would be invisible. Then I would fill with epoxy and drill new holes. Epoxy can be quite brittle, so choosing the right drill bit for the screw size is important--if it's too tight the epoxy might crack away and if it's too loose the table will not be secure.
Although many would consider the table to be mainly cosmetic, I think these tables can take alot of wear as people lean on them when sitting in the salon, or use them for support when walking below while underway, especially in rougher seas. Therefore, I think the table needs to be secure.
Others might chime in with better advice! Good luck!
Frank
1984 E30+