I'm sorry that I have to report a bug.
When I'm my browser window is small enough to make my menu and sidebar collapsed, and
when I use navbar-fixed-top class on my menu wrapper to make its position fixed without custom styling, and
when I use it together with the Off-Canvas sidebar,
the collapsed menu can be opened only if I don't click the icon for hiden off-canvas sidebar. Once I click the sidebar icon to open the off-canvas sidebar and close it again, the collapsed menu can't be opened any way, the button for opening collapsed menu just doesn't work anymore. But only when the conditions are met (see below clearly). I have to refresh the page to make the menu work again.
All these conditions have to be fullfilled in order to replicate the bug:
using navbar-fixed-top on menu wrapper
using off-canvas sidebar
menu is collapsed
sidebar is collapsed
browsing with desktop/android Chrome
after the menu collapsed icon AFTER clicking onto the off-canvas sidebar icon, if it's not clicked, menu doesn't get bugged
To be sure that it's not just a bug that I caused with wrong custom styles, I took your demo site ( http://demo.t3-framework.org/joomla30/index.php/en/ ) and added navbar-fixed-top class to the menu via developer tools in the desktop version of Chrome and made the Chrome window smaller to collapse the menu. Then I clicked on the sidebar icon, opened it, closed it. Then I clicked the collapsed menu icon and guess what, nothing happened, menu stopped working. It worked again even without refreshing the page after changing the browser's window dimensions.
I don't know if you are aware of this issue (couldn't find anything about it) so I'm reporting it. It's probably a JS issue I guess. I hope you'll come with a solution soon.
I'm using the latest Joomla 2.5.24, T3 Framework 2.3.2 and T3 BS3 Blank theme 2.1.6.
Thanks for your time.