The COM LED tells us what is going on in regards to the profibus communication of the master. If it is off it indicates it is not running at all. It is hard to say the exact cause with the limited info you have provided.
You might have the Control/status word on and not be putting the device into RUN. It could also be an issue where the profibus network is physically disconnected so it is not communicating.
Can you verify that you have downloaded a config with Nettool for Profibus? Does this configuration included slave with data mapped into the Anybus gateway?
PS it looks like you are from Europe, you can also submit a support case though your distributor or on mysupport.hms.se. This should get you in touch with your local support team.