99% Isopropyl alcohol (95% works too, just contains a bit more water) or electronics connection cleaner like Caig Deoxit. You can use a tiny brush (like a mascara brush) to clean the jack, or simply clean the plug well, then re-wet it with alcohol or cleaner and plug/unplug/rotate it in the jack to clean the internal jack contacts.
What I posted earlier is the first thing which comes to mind, a common problem, and will be good practice to do anyway..
..but I just listened to your sample and it doesn't sound like a dirty or intermittent connection because it seems to manifest as a quick clean fade, not as an immediate cut-out and has no apparent scratchiness or noise during the fade. That suggests an alternate issue such as a change of gain or loss of power to the mic capsule.