Help? Furnace eats transformers...

QUESTION:

I'm starting to think that my furnace is haunted. It seems to hate the humidifier. Why? I dunno.
Here's the setup: It's an ordinary Janitrol furnace. On it is mounted an Aprilaire humidifier (110 model). Both came with the house, so I don't know their history.
The Aprilaire unit plugs in to a regular 110v wall outlet for its power to run a fan and a water valve. There is a control circuit wired up with a humidistat (upstairs), a 110v/24v transformer, and a relay in the humidifier. The transformer is tapped off of the blower circuit in the furnace.
So, if the humidistat is closed, and the blower is on, the relay in the humidifier closes, turning the fan on and opening the water valve. When either the humidistat opens, or the blower turns off, the relay opens and the humidifier turns off.
Simple, right?
Well, except for the fact that every fall I have to buy it a new transformer. I've done this for the past four or five years. The primary side of the transformer burns out (verified with a meter, and visual inspection). Stranger, still, is that last year I got tired of buying new transformers, so I wired in a switch to the 110v supply from the furnace to the transformer primary winding, and I turned it off at the end of the winter. Tonight, I turned it on, and presto! the d*mn primary winding on the transformer is burnt out again.
I've tried using a cheap 110v/12v doorbell transformer. That burned out the secondary winding keeping the relay energized for long periods of time. I've tried buying real Aprilaire branded transformers. As far as I can tell, it works fine through the winter, but somehow magically burns out over the summer. Yes, I know, magic is impossible, but I don't have any good explanation as to why a perfectly good transformer would burn out while physically disconnected from the circuit. And, I would expect a transformer rated at 110v input to survive on a 110v circuit, even if I didn't disconnect it.
Any ideas? Am I just cursed? Should I buy a pallet-load of transformers and just consider them to be consumable parts, kinda like the filters and light bulbs? Is there a place I can buy a 110v/24v transformer that will survive more than 12 months in my house?

ANSWER:

There isn't much wiring to have a fault in. From the furnace controller, there are two 110vac wires (measured at 120vac +/- 1%) that come out to the blower motor. The 110v/24v transformer is tied in to this in parallel. Since it's the primary side of the transformer that goes, I don't think it can be anything in the 24v control circuit or the humidifier.
What's really puzzling me, though, is how it manages to burn out. I put a switch on the 110v side of this and turned the thing off. The only logical conclusions are that it burned out before I turned it off (possible, but I'm pretty sure it was working fine at the end of the winter), it burned out _while_ turned off (impossible...), or it burned out as soon as I turned it on for the year (why? beats me.).


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