Thanks for your suggestion. I looked through the link you provided.
I tried deleting the partition and creating just one FAT32 partition using gparted. I then also ( belt and braces !) reformatted the usb stick again in Windows as FAT32. Still no luck however getting TinyCore to mount the USB drive.
I came across another question in LinuxQuestions -
www.linuxquestions.org/questions/printthread.php?t=318392 which seemed relevant to my problem. This suggested making sure a volume label was attached - so I did this and it resolved a quirk in the way the drive was behaving in Windows but still no luck with TinyCore.
The mount command gives a "can't read superblock" message. The Fdisk -l output is to the effect the "Partition 1 has different physical / logical beginnings (non-Linux?)"
Finally ( it is a question of persistence after all !! ) tried a different brand ( two in fact ) and success !! TinyCore TCE's now persist on the non-Transcend sticks across sessions
So it looks like there is some issue with detection with Transcend USB sticks/TinyCore ? The Transcend sticks which I cannot mount in TinyCore work OK in Puppy linux, DSL and under Windows .
However I now have tce's carrying thorugh from one session to another so all is well for now at least - maybe the above will help to track down where the issue lies.
By the way - I did need to use the waitusb=5 bootcode