alt Hacker Newsi'd try to find out what is behind the reaction of the woman you are seeing. threatening to break up is in itself unhealthy for any relationship. if my partner thinks it is ok to make such threats then i'd end the relationship right there. if we are married then the next step is marriage counceling.
That's a really rigid way of thinking about it. Relationships are a negotiation, and if you stay in a committed one long enough you're going to find yourselves navigating some of these issues. If I'd only been seeing someone for a few weeks and their usual pattern was constant, immediate contact I'd assume there was something wrong. Some people tend to assume further that the problem is their fault. But that's a conversation you can have with your SO without giving them a counter-ultimatum.