Why is my electric wall heater slow to turn on and then quick to shut off?
I think it is one of two things.


The element is getting old and between the age and the moisture in the bathroom has taken the element close to end life.
The heater is 240V and maybe the breaker needs reset or it has gone bad or there is a bad connection in the heater.  I've seen wire connections fry pretty bad in some cases.


If it is the element and with today's technology, like camera phones and e-mail, you can probably work with Nutone to identify the heater, and Nutone pretty good about having parts like this on their shelve.  

Just be careful with the element, because it could be very brittle.  No hard bounces or dropping it or parts on it if you take it out.