I've been trying to fix this problem for the past month.
My wife has an iPad air with a Belkin QODE Slim Style (F5L152) that has been losing the space bar immediately after pairing. The space bar would work once each time and after that the only way to get it to work was to hit the back space once and then the space bar would work again ONCE.
This has been the same issue with 7.03 (on the iPad on startup), 7.04 ("upgrade" installed) and 7.1.
I paired the Belkin to my daughter's iPad 4 and it worked flawlessly. The iPad 4 is iOS 7.04.
After a month of frustration, I decided to try key combinations with the space bar and guess what, ALT + SPACE BAR corrected this issue. The space bar now works flawlessly.
I hope this helps others.