Ok - I think I have solved this.... it seems that this is a problem that many people have been frustrated by for a few years... surprising when you think that iTunes and iPods are Apple products.
I can't find the page now where I found this tip, but this is what worked for me:
Log into your account in iTunes
Go to Purchased
Choose TV Shows
In the bottom right hand corner of the window there should be a check box "Download HD when available"
Uncheck this box, then download your shows again
Then they should - hopefully - be able to be dragged onto your iPod