[northwind]

The inner core screws in, so it might not have been fitted right (it's normal to remove it when fitting tyres as it allows faster airflow into the tyre, which is helpful in fitting it to the beads- so maybe it's not been put back in right last time it was out. Or maybe it just worked loose).

So, you could possibly just refit the core, or fit a new one. But I wouldn't, personally, I wouldn't trust it. Replacing the valve means getting the tyre partly off unfortunately. The tyre should be absolutely fine though.