Same problem here using Tekkit 3.1.3
I can log in rarely, but if I disconnect then I get "Failed to login: Error" and have to wait.
I've tried removing all not required plugins. Didn't work.
Tried restarting the server. Didn't work.
Tried a fresh shiny new server with a fresh shiny new client. Didn't work.
Tried cussing at it. Didn't work
Just seems random. /cry
I want my blocky-goodness.