Michael's suggestion of running your own nbviewer instance is a good one I used in the past with an Enterprise Github server.
Another lightweight alternative is to have a cell at the end of your notebook that does a shell call to nbconvert so that it's automatically refreshed after running the whole thing:
!ipython nbconvert <notebook name>.ipynb --to html
EDIT: With Jupyter/IPython's Big Split, you'll probably want to change this to !jupyter nbconvert <notebook name>.ipynb --to html
now.