Why don't you try offering them a Tic Tac, if that doesn't work and their breath still smells like they've been eating shitt sandwiches maybe then it's time to call it quits. :):)
Have you talked to them about it? If you have and they did nothing to fix it, then definitely.
That is not really a valid reason to break up with someone
unless he/she has tried to resolve the issue without any avail and it is
becoming unbearable for you to live with this. The best thing would be to tell
the person, very gently, that he/she has bad breath because it is quite
probable that he/she is not aware of it.