Does iqdump from the GTM server to the LTM show traffic? (I suspect yes, because you have other VS's showing as up). If so, the comms are fine. I've had this incessently between GTM and LTM (Including co-hosted GTM/LTM). There's a nasty bug that's fixed in 11.2.1HF3 where big3d doesn't bother to send the VIP messages back to gtmd. In addition I've had this where VS's aren't members of any traffic groups or device-groups. And a funny one where VIP messages WERE being sent, but gtmd just decided they weren't being recieved for some reason... Not sure why that one went away (I eventually changed the Data Centre Objects associated with the Servers the VS's were members of and it all sprang into life... Again...).
Currently I'm all OK on 11.2.1HF2-ENG29... (HF3 has all the fixes except one for APM that I run though, and I havent' trued 11.3 yet for GTM issues).
H