These are the things we did that finally brought stability to our MS390's. We are running 14.32
1. Completely isolate spanning tree on Meraki network from any Catalyst PVST spanning tree using BPDU filters on the catalyst side and turning off RSTP on interfaces connecting to catalyst from the meraki side. Catalyst and Meraki STP do not play nice together on the MS-390.
2. After any L3 SVI changes (Adding removing, or moving VLAN subnets), reboot the entire stack. Other MS390 stacks on the network may need to be rebooted too. We just wait till the evening and reboot ALL of them. This is a known issue.
3. After updating to 14.32, make sure to reboot the MS-390 stack TWICE from the Meraki console. (Not just pulling the plug. FROM THE CONSOLE) The switch will take a long time and some strange lights will flash during one of the reboots. We suspect some type of firmware/rommon update is being applied quietly. But t6he switch will not apply this if you just pull the plugs or cycle power. it has to be a graceful from the console reboot to trigger it.
After all of this, they quit dropping off the console and have been relatively stable.
We also found in some cases with clients application layer firewall filtering on Palo Alto, Checkpoint, or FortiGate was causing issue with blocking management plane traffic to the cloud. Make sure the switch IP;s are exempt from any IPS/IDS or L7 firewall filtering or expect problems.
If you are using these as Data Center switches in a hosting environment where constant layer three changes are being made, you may want to consider Ronnies advice and get them swapped for native Meraki switches as the constant rebooting may be unpalletable.