I'm using suggestionbox with JSF Sun RI 1.1.01 and found the issue.
The suggestionbox does not appear when entering a symbol in case if minChars set to 1. It appears just after three symbols entered.
It works fine with JSF Sun RI 1.2.
If you need to use jsf 1.1 try please to update to jsf 1.1_02 - which is highly recomended instead of *_01version.