This is really just my perspective, so you may want to take it with a grain of salt.
To say it 'isn't working' is a simple statement of fact. (It could be that the service is down.) To say it 'won't work' would mean to me that you're trying to get it to work but something's preventing it from working properly. (So the service is working properly but you're having problems on your end.)
This is a relatively minor distinction and most people will use the two interchangeably.