Good news! I was having the same issues discussed above. Freezing and restarting every time after about 3-4 of fine live streaming. I had a lengthy Twitter message back and forth with MLBTV support. It eventually ended with them saying LG is aware of the issue and is working to resolve it with the next software update. BUT! They told me to try one last workaround that proved successful for me.
1. Change the input on the TV to "Live TV" even if you don't have any signal/antenna attached to that.
2. From there, browse the LG smart hub to the MLB.TV app and launch a live stream. (From here, the problem was solved for me and I have yet to have a freeze.)
They also added: 3. If you are still seeing issues, remove all HDMI cables connected to the TV and ensure the TV is set to “Live TV” for input.