Horray!  Someone else trying to get their own base station working!  I have the same setup but I'm running SNIP myself and not using RTK2go.  I did for testing and then quit using it.

I've been told that the "dropping" of the connection to the caster that you see within the Mosiac interface is not accurate.  It doesn't really drop.  I see it with all three of the places I send data to on with two separate boards.  The stream into my SNIP caster is steady from both boards.

BUT....I am dealing with something similar to you.  I've posted here about it but I'll try again.  First, my system works absolutely perfect on all my units if I use a cell phone or tablet as the communication device.  One devices uses a built in NTRIP client and two others I can use an XBEE or RTKonnect device tethered to a phone.  I can hold an RTK fix all day long (with XFILL turned off).  I also have a CaseIH tractor with a Vector Pro connecting with its one cellular modem and NTRIP client.  Absolutely ZERO issues with those setups.

My issues arise when I try to use the Ardusimple 4G NTRIP Master with a T-Mobile compatible SIM card.  They seem to be very similar to your issues but movement doesn't make a difference.  I'll get a perfect fix for 1-10 minutes and then loose it for 1-10 minutes but according to my caster it never disconnects.  I've ran it on my desk and watched the status lights for days and the cellular signal never disconnects but I do notice that the Serial TX light does not flash consistently.  Baud rates don't appear to make a difference.  I'm thinking it is a latency issue with the T-Mobile network (or the discount SIM) I'm using.  Unfortunately the board is not compatible with Verizon.