OK well I have had a problem with the launcher for over a week now one being “connection error(s) detected. retrying” and another being unable to download the game from scratch from the GW2 website, the launcher says “download failed. please check your internet connection”.
I just now tried a fix that I was certain would not work but to my surprise it did work and fixed the problem, thought I have to install the game from scratch which if any are like me I don’t think you will mind.
I of course take no credit for this I am simply passing this method along to those who have not yet tried it.
http://www.guildwars2guru.com/topic/38407-stuck-beta-launcher-screen-with-checking-for-updates-and-no-firewall-answer-here/
I hope it works for you as it did me.