I'm still investigating and it appears that there is no problem with JAudioTagger. Before setting the tags, I use Total Recorder to reduce the quality of the download from 128kbps, 44,100Hz to 56kbps, 22,050Hz. This reduces the file size to less than half and the quality is fine for speech radio.
If I run my script on the original files, none of the audio track is deleted. The deletion of the first part of the audio track only occurs with the files that have been processed by Total Recorder.
Looking at the JAudioTagger logging for these files, there does appear to be a problem with the header:
Checking further because the ID3 Tag ends at 0x23f9 but the mp3 audio doesnt start until 0x7a77
Confirmed audio starts at 0x7a77 whether searching from start or from end of ID3 tag
This check is not performed for files that have not been processed by Total Recorder.
The log of the header read operation also shows (for a 27 minute track):
trackLength:06:52
It looks as though I shall have to find a new MP3 file editor!