Let's begin with the following premise - a relationship is an agreement between two people who are attracted to each other and want to spend time getting to know one another.
Included in a healthy relationship are respect, kindness, communication, compassion - to name a few. This is what you owe yourself and your partner - your best. Not perfection, but awareness, willingness to consider another perspective and humility. In this way, you elicit the best from yourself and your partner. When there is a misunderstanding or another type of bump-in-the-road, your relationship has the foundation to resolve any conflict either by communicating, allowing the other their space - if necessary, in general, a safe space to process whatever is happening.
Moreover, another person that you value and love will be one who is happy for your victories and supports you through your tough times. Your partner is someone who values who you are, may roll their eyes at your quirks but appreciates what makes you, you.
By the same token, you also share in your partner's successes and encourages them when they stumble. Each of you helps the other to grow as a person and enjoys each other's company. Each feels like an important part of the other's life.
Signs the relationship has stopped moving forward can include - cheating, increasingly hurtful exchanges, distancing (emotionally, physically, sexually). When you and your partner have stopped relating as a loving entity - a team, that is usually the first sign. To quote a decades-old song - "You've lost that loving feeling". When that has happened, you know that something needs to be addressed.
If there isn't a way to address problems or if you have and the relationship continues to stagnate, creating more conflict than happiness, it's time to go.
A word about breaking up - It should be done in person. If you are long-distance, there still needs to be a concerted effort to break up with someone in person. If only one feels like they want to end in person, the other should comply. Breaking up via post-it, phone, email, text is cowardly. Note - we are not discussing situations of domestic violence, etc.
There is no art or skill to breaking up. It sucks. Someone or both will be hurt. You can be clear, firm, kind and compassionate. It doesn't need to drag on but being understanding with someone else's feelings is never a waste of time.
Staying in an unhappy relationship because of guilt, sense of obligation or pleadings is disrespectful to both parties. Each needs to have the ability to move forward in life.
Moving forward after a breakup is always hard. It is like a death. You need to take care of yourself, sleep, be with friends, talk to a therapist if your sadness is interfering with your activities of daily living - work, hygiene, etc.
There is a Zen proverb that says... "Let go or be dragged".