Like most aviation answers, it depends.
Before starting the approach you should have an idea of what the weather is.
If the approach has a localizer only minimum-which most do then( assuming the ILS has been properly tuned and identified and you don't have a VOR frequency tuned in -which has happened, more than once): check the locailizer flag, check the F/O HSI if no flags then continue to loaclizer only minimums. IF BELOW LOCALIZER ONLY MINIMUMS then a missed approach must be executed.
On ILS approaches I brief the ILS DH and the LOC only MDA or NDB which ever may apply, with the expectation of continuing on to LOC minimums if the GS is lost.
One airport I flew into regularly had seasonal problems with the GS when in the spring the snow melted during the daytime and then the water froze at night causing havok with the GS transmitter.
In any event its no big deal-unless the weather is 200 with an RVR of 1200 ft (400 METERS).