How can I fix Ubuntu Minecraft constantly turning off fullscreen?

I use Ubuntu also, and I experienced similar problems. Generally, I found that full screen mode flickered a lot in Ubuntu, and although I didn't have your same problems, I was having a generally bad time.

I'd recommend going into compiz-config (It should be installed by default, if it isn't, install it), going into OpenGL settings, and make sure that OpenGL is actually on. I know, you didn't ask this question specifically, but I'm telling you, you will experience this issue later on :D.

As for your specific problem, you have two options really. The first, simpler one is to rebind your keys. I have my sprint key set to X not CTRL, because CTRL will often disrupt me XD.

The harder way is to go into Settings Manager > Keyboard > Shortcuts and looking for & disabling the CTRL-Space shortcut, whatever that does.

I'm guessing what's going on is CTRL-Space is opening some window or doing some thing the sets the window focus to the desktop, and when that happens, Minecraft will automatically exit full screen mode (This is an actual feature of Minecraft, not Ubuntu).

Hope this helps!