[SPCh]

Back in ancient times we used to have a very effective glue-free fix.
If the plastic-with-pins base was simply loose (i.e tension on the pinch wires was just slack) we'd wind a piece of 16swg copper wire round the glass at base level. This would force the base downwards, take up the slack, and stiffen the whole thing up. The shape of the glass was invariably "sympathetic". One or at most two turns, with a drop of solder on the twist to hold it firm, usually solved the problem.