I notice this problem even before the release of S7, I think this problem started around when the Starbases were launched.
I have had the same problem with my chat since the second or third week of August. I have submitted 2 bug tkts and also opened an in-game GM help ticket. The GM tkt says they think its a bug since I can still see a random post here and there, but they still haven't fixed it yet.
I can get around this by adding ppl to my friends list but that is the only way I can talk to ppl outside of my fleet. I also verified I was NOT perma-chat banned. If anyone else has experienced this and has fixed it, I would sure like to know.
"STO is like a box of chocolates, you never know what bug you're gonna get."