I found that if I hold down the RESET button while applying power to the Betz board, that the problem goes away for a while. I wonder if it's related to how the DTR line on the FTDI UART is connected to the RESET pin on the bluetooth chip through a capacitor. Perhaps that capacitor is building up a charge some of the time and it needs to get discharged once in a while by holding down the reset button.

http://www.betztechnik.ca/uploads/2/5/6/7/25674051/wt32i.pdf