My gizmo disconnects from time to time - I can reconnect, but there's no recollection of where I was. Listening to an hour long podcast is difficult to resume as there's no bookmark, last position, or a way to select based on time, one can just tap a position as a guess, without an indication of the time into the track.
You mention this happens when you get a text. This may be related to the biggest pain point for me which prevents me from using Gizmo and JRiver for what I wanted to - namely a replacement for Google Music and other apps: It doesn't run as a service that stays open, so Android shuts it down to save memory.
Most media and streaming apps (all that I've tried, at least), keep the app as a service in the tray. Think Google Music, Audible, Pocket Cast, Amazon, etc. They all sit on the tray and show you the current status, so you can see that it is running. Without an app being programmed to do that, Android will shut it down to save memory.
For most apps that's not a problem as they will preserve state, but JRiver Gizmo doesn't do that either.
All of this to say: I don't think it's a reliability issue that I have, just some design flaws that I'm sure are known to JRiver and must be under development (though I've never seen an update to Gizmo in the Play Store.).