Magnetic coil failure
It can be a localised spike in temperature, as Ignacio says in the comments, that easily melts such thin wire.

MOhm for a small inductor coil means completely broken, certainly if it used to be Ohms.

It can be that the increased temperature was from using an inefficient frequency, but, since you aren't referring to any current known or observed, I'd say it's over-current.

If you look in this PDF you can see that for simple chassis wiring or a bundle for power transmission the current limit for AWG40 is already in the tens of miliAmps, and they just don't say for enything tinier. I would estimate the limit for AWG46 will be around 25mA or so, if not lower. 

And that's only for a couple of wires together for a coil you need to lower that, usually by at least 30%, depending a bit on the coil shape and build-up.