how can you save an on-the-rocks relationship?

Both parties have to be willing to save it. In order to save it you need to identify what's causing it to falter, and find ways to work on fixing those problems. Compromise is definitely a friend here. If only one person works to save it, it's not going to work. If you can't accept the compromises, it's not going to work. You must realize that all relationships are on the rocks at some point or another... and if you're running into the same issues a lot, is it worth it?

relationship should always be a two-way traffic, and in order to save a rocky relationship both of the partners should be willing to compromise.

If both people want to save their relationship,yes it can be saved.They may need counciling but it can be saved.When one partner wants to save it and the other doesn't, that's when it can't be saved.

Both partners should be committed to trying to save their relationship. It generally will not work unless both give a little. They need to be able to talk to one another, discuss any problems rationally without yelling, accusations, calling of names, they need to be able to communicate how they are feeling, what needs to be worked on, etc... Relationships are not one sided, both parties in a relationship need to be able to discuss things, including their feelings, their likes and dislikes, and agree to compromise. I wish the best to them and hope they can save their relationship.

It can work but both people really have to want it to. If the sincerity is'nt there from both parties it's impossible. Make your decisions carefully because it could be a big waste of time even if both people try. If it has gotten to this point and there are no kids involved a clean break might be the best way of handling it.