Since i do not know exactly what type of method is used to create resistance because i don't know the exact model i am going to guess by an electromagnetic process. any time electricity is used to create resistance more power is needed when more resistance is desired. the additional power creates heat as a side effect. many electrical circuits employ the use of an over heat protection circuit (like an over current protection circuit). now that you are desiring more resistance and for longer periods of time it is possible that the trainer's protection circuit is kicking in to save itself.
the next time this happens you might try feeling around to see if the trainer feels hot near wherever the resistance unit may be. i have a kicker and after a long ride with lots of resistance i can feel a good amount of heat on the flywheel once it stops moving. if you do find that it is getting hot try aiming a fan on it to see if some additional cooling will let you ride longer.
this is not a solution, only a way to determine if it is overheating.
this of course is just a complete guess but an educated one from experience with some electronic devices.
-scott
ps. i used to live in Bury St. Edmunds. i miss it there sometimes.