Hi PhoneLady, and welcome to Mitel Forums.
Unfortunately, I don't know that I can be a lot of help here, even with more information. Before contacting support I would try to narrow down the circumstances that cause the "silent" calls. It sounds like it is always calls that originate or at least are flowing through the 6510, but it is hard to tell.
Support may know of issues with your particular versions of the 3300 and the 6510 so might be worth talking to them.
Good luck!