When you check the connector status, can you also take a look at that agent directly in Manage > Agents, then Gear for that agent > Connectors? It would be good to make sure that the Ops Center dashboard is reporting the same data as the Agent itself.
Are any of these agents in Connector Profiles?
Lastly, the agent log from an affected system may be of interest. If the connectors really are stopping, there should be accompanying errors. You might also see them in your LEM console, or if you expand the timeframe in that bottom chart to longer than the default (you probably need to go to last week) it would be interesting to know what the most recent message is.
Thanks for the reply, I´m already working with support for this.