I had this issue recently. When I first started using Technic I never had issues logging in, until about a week ago. I was "Unable to connect to minecraft.net" the launcher would say, every time I went to play.
I tried to fix it by first making a backup of my .techniclauncher folder and deleting the lastlogin file. No dice so I restored the backup and tried just clearing the cache, still no luck. I then deleted the whole folder and tried redownloading everything, still no luck.
I restored my backup then checked the forums, and after trying to log in with my e-mail that I used for my Mojang account I no longer have the login issues.
My guess is that it isn't client side, or the launcher. Mojang must have changed something in their authentication system.