I have exactly the same problem. So annoying! But I think this is a launcher bug not a tekkit classic bug, and you might have seen the post about not mixing the two up. You may want to consider relocating this to the launcher bugs section so it gets more attention and you don't risk a ban?
Personally I am dying to see the issue solved. (I'd just like to say that this only happened to me after I messed about trying to create a server. When it didn't work I gave up and for some reason reinstalled the launcher. Not sure if it's related?)