The flasher relies on a current load to heat up and flash. If it no longer heats up, it may not flash, but will still allow the lights to light.
But there are other things that will make this happen. Low battery for one. Our vintage of bikes are notorious for not having enough current to run everything if, say you upgrade to a 55/60 Halogen headlight. Or, as the bike gets older, corrosion appears and less electricity gets to where it needs to be.