It may feel natural for you to ask this question, but it may not be the most helpful question to ask. It is simply not a given that every relationship can work out, or is best to be continued for the people involved. For simplicity I will focus here on the relationship between one and another person, though I am well aware that more complicated (group) patterns are possible.
Your personal position
I definitely think that psychotherapy can help you to sort out whether you want to stay in a particular relationship or not. One element may simply be talking about it with another person, saying out loud your worries, fears, concerns, and other feelings you have about the relationship, what happens in it, and what your partner does. Psychotherapy is a good place for this. And there is also place for a more mundane listing of practical considerations, listing the pros and the cons. You want to know, when considering breaking up, whether you think you will be better off or worse off in all respects, if you would do it.
The wider context
In addition it is always worth putting the idea of the relationship ending in a wider perspective. What will you do when you break up? Will you have financial concerns? What effect will it have on your circle of friends and contacts? What about a place to live? Are their children or other dependants involved? ill there be an impact on other circumstances? Contractual aspects? Is there a split-up process that is long and costly or that worries you, such as divorcing when you are married? Does splitting up have particular consequences in your church, religious or spiritual community?
None of these should fully determine what you will do, or will plan on doing, but all of them are worth bringing out into the open and considering. In my view, none of them are as important as the first line of consideration: how the relationship itself works out for you personally.
It is only after this essential weighing off and consideration process, and if and when you have taken a decision that you would want to continue a relationship that gives you or your partner difficulties, that you can think about using psychotherapy to "save" the relationship.
You need to engage and communicate
When you have reached that decision, the next step is to realise that you cannot decide on your own, independently. The essence of a relationship is its jointness, its mutuality. You will need to involve your partner in the process, and communicate with him or her, as part of the process of "staying rather than leaving". In this process a psychotherapist can definitely help, but cannot "fix" things.
How to use psychotherapy
How can you use psychotherapy to influence / improve a relationship? Basically there are four models:
- One partner can have individual psychotherapy
- Both partners can have psychotherapy
- The partners can jointly visit a couple therapist
- It is possible to combine some of these options, e.g. do couple psychotherapy and individual therapy.
The last option may perhaps be effective, but seems a bit of a blunderbuss - in my view there need to be special circumstances or reasons to justify it.
It is an important realisation, that you can work on a relationship through individual therapy - many people forget this or are not aware of it. There was at one stage a whole institute for relationship therapy in the US that specialised in that way of working, and who thought that this was more likely to be successful than couple therapy with both partners in a room.
Conclusion for action
First analyse what you need and what you want. Then act on your conclusions. Some patience, some sitting on problems and reflecting on them, can have its uses. But overall, things will only happen when you act. That can feel very uncomfortable, but it is worth acting to improve your life. Relationships are amongst the most important aspects of life. Don't let them simmer and fester - be an agent of change, and an agent of hope!