After responding with a similar experience earlier in this post, I think I've figured out a workaround. As I mentioned, I only see the problem when not in turn-by-turn mode, but just displaying my current location - it's during that mode that the map freezes and my location leaves the map displayed on the screen.
After much testing, I've noticed that this happens only when I'm in the orientation mode of direction-always-up. That's the orientation where the map turns to always show your direction pointing towards the top of the screen and the orientation icon is the filled-in arrow, pointing north, WITH the circle around it.
When I put the orientation in the North-Up mode so that the map never rotates, but the direction indicator turns to follow the map, I have yet to have the map freeze up on me. On CarPlay's GUI, this means setting the orientation icon to the filled-in arrow pointing northeast, WITHOUT the circle around it.
I don't prefer this mode to always facing north, but it has yet to freeze up on me, so it's a tradeoff.