In case anyone else has this issue, I got a thorough workaround from OLPC support (not using the VNC Launcher activity). This worked:
1) Switch from Sugar Learning Platform into GNOME (hover over Sugar's central XO figure -> My Settings -> Switch desktop -> Switch to GNOME)
2) Launch Applications -> System Tools -> Terminal
3) Type "su" and hit enter
4) Type "yum -y install vino" and hit return. You'll need to be connected to the internet.
5) System -> Preferences -> Remote Desktop
6) Check "Allow other users to view your desktop", "Allow other users to control your desktop", uncheck "You must confirm each access to this machine", check "Configure network automatically to accept connections"
7) Switch back to Sugar -- "Switch to Sugar" icon on desktop
In Sugar, launch "Terminal" Activity; you will need to click on the "List view" in the top right. Optionally click on the star to the left of Terminal in the List view if you want to add this Activity to your regular "Favorites view"
9) Type "/usr/libexec/vino-server" and hit enter
10) You can now connect to whatever the IP address of the XO is, with a standard VNC client running on any other computer on your local network. (You can find out your XO laptop's IP address with "ifconfig"