Basically, I am able to connect fine and stay on for (as far as I know) as long as I like as long as there's not a lot of talking. However, once the chatting starts, I would lose connection with the server and fail to connect with it unless I closed Teamspeak and then launched the program again...and the cycle would continue.
Apparently, in the thread linked above, it's caused by this:
Router / Firewall detected too many packets on the port used by the client and decided to drop Packets on the Port the Client uses for the Server you are dropping out of. The reason it works again (for a short time) on new Tab or with newly started Client is that a different Port is used.
Check your Router / Firewall for an Option that says something about Flood Protection / DDoS Protection or the like and turn it off.
I have an Orcon GeniusLite and I've fiddled around with it but did not dare to make any changes because I wasn't exactly sure what it would do or if it was the right thing to do. I've figured it should be somewhere in the Advanced Settings part, but whether I should mess with the Firewall or the Application sections is beyond me.
A little help sorting this out would be very much appreciated.