If you're using Chrome...
Thru searching for a cure to my own spacebar problems, I came across the fact that Chrome (especially) has had spacebar issues with Flash apps (particularly chat) for years.
The spacebar is usually used to scroll the windows in browsers, and disabling this in a chat window (giving the chat window exclusive focus to the spacebar's intended use) seems to be a tough fix. The inability to insert <spaces> between words in chat is reportedly a related issue.
I've had some success by using the "Iron" browser, instead of Chrome, while playing the game.