Are the agents themselves online? Generally connectors are auto-start and the only thing that causes them to stop is an error.
Also, if you're looking at the "Node Details" area in the Ops Center area, I'd also check Manage > Nodes and then Gear > Connectors on that agent. We've seen reports that the "Node Details" area reports out of date information, i.e. is not aware that the connectors actually ARE running.
Now, if the connectors are running but not reporting data, that could be something else entirely. You might try something as simple as restarting the agent.
I have six domain controllers in my enviroment which I have created a (group) connector profile for. Five of the controllers log alerts, but I have one controller that repeatedly disconnects. The LEM depicts this controller as disconnected and I do not see any logs being generated. The SW LEM service stops running on this controller and will not start backup. The only temporary solution I have found is to uninstall and reinstall the agent. I have looked in the SPOPlog file but I have not found any evidence that points to a possible issue. Where else can I look to collect informtion that will help solve this problem?