May or may not help, but try placing the mic in a zip lock plastic bag overnight with some desiccant packs. If your environment has dampness in the air, some may have settled onto the capsule and causing some electrical leakage that presents itself as the noise you hear. If you don't have any desiccant packs, substituting with some dry rice in a stocking will pull moisture out of the mic also.

Thanks, Mark. I will give that a try!

seems to be that all my condenser mics have dessicant packs in their cases already, but none of my dynamic ones do.
what did the 4040 come with?
i wonder if they do this to suck up errant spittle as well?
ew
mics are gross man...

That problem is always a problem here in the South. Besides the above suggestions, I have used a hairdryer on "low heat" to de-humidify mics. Just be careful to keep the air moving and don't concentrate it on the capsule. I was told by an AKG tech rep many years ago when I had this problem with a pair of C452's that the humidity was affecting the FET's in the active circuitry. This might be why dynamics don't ship with dessicant...no active electronics in them.
I have a few 40-series LDC's never have had a problem with that. And , yes, they did ship with the dessicant packs...

I've fixed microphone static by cleaning the microphone's XLR pins with 99.9% isopropyl alcohol and following up by applying caig deoxit D5 to the pins.

Might not hurt to hit the cable connector with some deoxit as well with a wetted pipe cleaner or similar. Good to hear you found a fix. I've had a few 1/4" plugs and jacks that got wonky in the same way and that deoxit is great stuff.