OK, this was resolved. It is weird, but some of my timers on the T4 did not have a channel associated with them. IceTV had a channel in all its entries, but the T4 did not. In particular, there was one at the same time as the shows giving the errors.
Editing the timers to add the correct channel gave lots of errors, but did the correct thing, and all the problems disappeared.
I did retune the T4 a few days ago, after an antenna move, so perhaps these were existing timers, whose channels moved somehow and disappeared - I don't know how the T4 identifies a channel internally.
All good. Thanks to all those who made suggestions.