Here's how I fixed a problem I've been having recently with Google Chrome searches from the Omni-box.
The symptom was that I would be typing my search at the top of Chrome when Google would suddenly complete the search for me. The search string Google chose would usually be nothing like what I was after, and often the search box would have disappeared. I would also notice the message 'Google Instant is unavailable' just before it happened.
The fix was to go into Google Search settings (click the 'cog' icon on the right-hand side of a search page and choose 'Search Settings'), and look at 'Google Instant predictions'. I was set to 'Only when my computer is fast enough'. I changed this to 'Always show Instant results' and the problem has gone away.
Supplemental - since then the problem has started again. I think the fix above helps, but I'm not really sure.