Is the maximum parking for three hours?
Within the confines of that pass?
In that case, they are right I'm afraid.
This is an extension of the 'feeding the meter' argument.
When your pass time runs out you are under a duty to leave. You cannot place another pass on lawfully or add more money to the meter should that apply.
The reason it rarely applies is that it is near impossible for the council to prove that people have done this. If they can in this case then it falls away.
Can I clarify anything for you?
Not in this case unless the first permit would have covered you at the time of fining.
Even then it would only provide a defence if they had done that without notifying.