Try cycling power on the N2K network, which is probably powered separately from the Garmin. I'm not familiar with Garmin gear, but in most other systems the N2K network has it's own power source, so cycling the MFD doesn't reset or power cycle N2K, and hence not the Airmar.
When you access it directly via a phone app, what does that mean? What app, and how is it connecting to the N2K network? If it's a Garmin app, then it's probably taking to the Garmin MFD, and accessing N2K data that way. So if the issue is in the Garmin, I wouldn't expect a Garmin app to work either.
I have no idea if this is what you are encountering, but in the past I have heard of issues where other devices choke on the Airmar data. Between the weather data, and assuming your model has it, GPS, tilt,heading, and rate of turn, all of which update at relatively fast rates, it pumps out a lot of data. I think it's largely adjustable through the Airmar program which is called Weathercaster, but to run it you need an Actisense USB to N2K adapter, and the program runs on a PC.
In general for debugging N2K, I have found Maretron's N2KAnalyzer program to be very handy, but it requires a USB100 or IPG100 device to connect your PC to N2K. And also Actisense's NMEAReader program, which requires an Actisense NTG or NTW (I can never remember which is the USB to N2K device) to run. So with either or both there is a hardware investment to make the tools work. I'd say I use N2KAnalyzer 60-70% of the time, and NMEAReader 30-40%. Each has strengths and weaknesses.