Same here, same issue. Something different though is that it occurs for me like this:
I logged onto my tekkit server, which I am normally able to use fine. My friend also uses the server, but does not experience the problem I am about to describe. Then, after playing a bit, tekkit randomly freezes and crashes. (Looking through the server log I found it was an end of stream, for I got no error message when it crashed). I load up the technic launcher again and it says "cannot connect to minecraft.net", though regular minecraft works fine. I did find a way to work around this a little though: I cleared the cache completely and it was able to connect, until I crashed again.
EDIT: Never mind on the clear cache thing, just tried it again and it didn't work. Not even totally re installing tekkit. Also had an idea: this only happened to me after tekkit upgraded to 3.03 and the server tekkit upgraded to 3.04. Connection?
