demagnetising a magnet with a high frequency transformer
It is unlikely you can reach the coercively levels required with high current magnetic induction without extraordinary efforts. 
will it be demagnetized?   No.   Even 1kW speaker magnetics won’t be degraded.
Will a progressive increase in the electromagnet's frequency at some point potentially demagnetize the permanent magnet? 


No. rising frequency reduces the current which reduces magnetic field .

But if you heat it up to the Curie temp. from winding losses,  it will lose magnetic strength.

Since Impedance of an electromagnet= 2pi f L the strongest field is a low frequency and the frequency response or inversely, the slew rate is determined by the L/R response time (Tau).