Well then you have learned not to deploy from github, get an AWS micro instance which you can also push to and deploy from that or many other possibilies that a Dcvs gives you.
Keeping code in sync with your colleagues should not be a major problem, given how you should be able to sync with each other (distributed CVS, etc). Azure... I don't know how that works. Heroku would work without github being online, since you'd push to github - maybe that'd be an idea?
bower_install is annoying, yeah; it should allow for a backup location (s) to resolve dependencies. Maven allows people to configure multiple repositories, which are often mirrored against each other while hosted by vastly different parties; if one repo mirror is offline, there's a dozen others available, in a lot of cases.
For those components, github is a single point of failure.
While GIT is distributed, working collaboratively with others still requires a central platform where everybody working on that GIT repo can connect. GitHub is a very convenient central platform.
To GITs credit; you can, with a little server know-how, set up your own git server and give all previous contributors access. However for a small downtime this could be overkill.
And even if you don't want to use a dedicate git hosting service, good site hosting platforms (Webfaction) make it incredibly easy to install a git server.
We can't push latest bugfix to GitHub. Azure cannot deploy it. I cannot run bower_install on the project I would be working on in the meantime.