I thought I'd let everyone know the outcome of my problem.
I took the device into the local Sony repair centre before Christmas and got a call to say they'd fixed it a couple of days later. They had done a "factory reset" and they said it was working now. As I'd already done a factory reset I know this was not the case but you can't argue with them.
So I went in and picked it up, plugged it into my usb charger in the car on the way home and 2 minutes later it was cycling (reboot, whirly circle, reboot) again so I took it straight back and they said they would replace it this time.
With delays due to holidays and lack of local stock, I finally picked up the new reader last week and since then, it hasn't missed a beat and I'm well happy with it!
So, if your PRS-T1 is crashing and cycling it's a hardware fault and the device needs to be replaced.