Is this problem still occurring?
I'd like to help but am completely unfamiliar with these microphones. Assuming that the outer housing of the microphone is made of metal, is there a metal screw (or more than one) that holds the housing on to the innards of the microphone? If so, have you tried tightening those screws, and making sure that they are contacting a clean metal surface on the innards of the microphone? You want to make sure of unbroken continuity between the microphone housing and (via the output connector) the cable shield. Even small gaps can make a difference at radio frequencies.
But if this is a "remote capsule" type of microphone as Jon Stoppable's reply suggests, then you're in risky territory to begin with. Such systems generally use unbalanced cabling and connections which are inherently much more vulnerable to RF than balanced cables and connections. Not sure what to tell you in that case; there are some environments in which such microphones just can't be used reliably, and increasingly so with the proliferation of cell phones and mobile devices. On the other hand, the radio signals may be entering output of the microphone amplifier, which is balanced, no?
I would also suggest giving A-T a call. While their stuff is manufactured overseas, they have a major home office in Ohio with technical experts on hand, and they seem to be a customer-service-oriented company from my dealings with them.
--best regards