People who have committed to a long term relationship are expected to care about their partner, but compassion is even more important. Every person has their own outlook and needs in life, and this does not change when a person enters a relationship. If a partner's needs are not being met, there is little reason for them to remain. It may be impossible to satisfy every need of a partner, but taking the time to find out what they are and attempting to satisfy them may be enough to keep the relationship on track.
Not all people are sensitive, and it sometimes takes a while to get their attention on an emotional issue. This does not mean they lack compassion, it simply shows they do not recognize a particular need. Once a person has been shown the need for empathy in a particular situation, their response indicates whether or not they have enough compassion to be a good partner.
Attempting to understand a partner's needs in life is important, and handling their requests in a kind and tolerant manner shows compassion. It lets a partner know their point of view is important, and it also shows they have chosen to be with someone who truly wants their life to be successful and happy within the relationship. A partner who dismisses important issues or needs has shown a lack of true compassion, and the relationship may fail.
While being compassionate is important, it does not obligate anyone in a relationship to be used. A person who has issues needs to solve them, and intolerance of their failure to do so does not signify a lack of compassion. This is the type of compassion that leads to people saving themselves from a co-dependent relationship, and it may be best to end any relationship where compassion is expected on even minor issues.