As you say, possibly a siezed motorised valve keeping the CH on if it has such a thing.
Often in older systems they just turned the pump off when CH not required and they could then circulate a bit by gravity.
Sounds worth investigating the header tank, if it has one. Often they'd have a primatic hot water tank by which means the CH would be topped up and they're properly bonkers, and very prone to getting the system in a bad way if the primary and secondary water don't stay separate.

Does she have an immersion heater that would cover the hot water demand this time of year?
Kevin