The last thing a mortgage company want's to do is repossess, not out of the goodness of their harts but because over the lifetime of the mortgage they will be making loads of money out of it.
The best course always when you have trouble paying the mortgage is to tell the mortgage company as soon as possible, as bednobs says they can help out if the situation is temporary and are far more reasonable if you are up front and honest about the situation.
So the answer to the question is generally yes, but of course will very much depend on the circumstances.