Sounds like the Comm. program isn't sending very fast. Sometimes these DNC Programs don't handshake very well, and they prevent buffer overflow alarms by putting time delays between each character. If you have any time delays in your DNC system settings, try setting them to zero and see if that speeds things up.
The Fanuc controls handshake with Xon/Xoff, and they should accept data at about 9600 baud with no troubles. If the DNC program is a good one, it should have no problem sending data at 9600 baud.