Dr. M T Thomas,
What you describe is a common problem with the uBiTx line of transceivers. It is most often caused by RF getting into the rig, most likely from either the microphone cord or the coax shield. The best way to verify is to connect to an RF dummy load and see if it happens then. If it does not stick in transmit mode, then it is RF getting back into the microcontroller.
Two solutions and both can be done.
1 - Put a common mode choke or snap-on ferrite in or on the coax from the antenna. This is to keep RF out of the radio/shack.
2 - Put a snap-on ferrite on the microphone cord just before the plug and/or add 0.1 uF bypass capacitors on the PTT and microphone input.
Also, be sure that you have good earth ground on the case of the uBiTx.
It always helps to include the version of BiTx when asking for help on this site. There are multiple models and versions of the BiTx radios, and the best solution can be based on which one you have the issue with.
Hope this helps.