It is interesting to note that she mentioned a gas fireplace and you've got it on a stand. You might have a wall furnace or floor furnace that's burning or venting improperly. This can actually be a major health concern if it's not burning right or worse, letting too much CO build up in the air.

I am a chemistry teacher in my spare time, and can help out a little bit with some of the answers. First of all, what is tarnish? Many metals will oxidize, in otherwords combine with oxygen or other elements to form a new compound. Silver readily forms a compound with sulfur to form Silver sulfide, the really black tarnish on silver. Using a chemical treatment will remove the tarnish, but at the expense of washing away some of the silver. On a plated instrument, that wouldn't be so good, and on a solid or sterling silver it might cause micropitting. That's why some people use a treatment that actually produces a reaction that gets rid of the tarnish and replaces it with new silver.

Some of you are right in that it matters what metals are used to combine with silver to make the alloy or the plating solution. Copper is closest to silver chemically as is gold. Unfortunately, gold is a lot more expensive than copper, so it is not used as much. Plated instruments may be over brass (which is a copper alloy) or the silver layer may be applied over a layer of copper which binds it better and actually makes it "shinier". The other metal they may use to mix is nickel, either in the silver plating material or as a base surface. Many people are allergic to nickel or they have sweat that reacts with the nickel. That comes out an ugly green color.

Some instrument makers put a lacquer surface on their plated instruments which make them shinier and protect the surface. Your instrument repairman may also have used a harsh chemical treatment that may accelerate the problem. You may want to look in to finding a reputable firm that specializes in silver plating instrument keys, and have them silver plated or even gold or rhodium plated ($$$!!!)Gold, platinum and rhodium are fairly unreactive elements, which is why they are prized for jewelry.