Looks like your "server" (the system where you administrate Awesome Miner) can not connect to the client. You can test clicking on "Test connection" in Options -> Managed Hosts -> Edit (Your Miner).
The clients normally do not stop mining on their own, if there is no connection to the server. They are even able to start the software after reboot (if configured) even when the server is offline.
Greetings