As has been said elsewhere on this site, making and keeping our connections to others remains one of the fundamental arts we learn in life. And having a stickybeak into other people's relationships is one of the fundamental past times. This isn't always so gratifying though, because relationships don't always work out. Alongside his beautiful model of coming together, Mark Knapp also developed a beautiful model that describes the process of coming apart. There are others with more specificity, like this one, but this model describes the predictable patterns of relationship breakdowns in broader terms.
At first, the two people start to become separate. They start to detangle themselves from their other. They'll share less activities and develop separate friends. The similarities that were developed over the course of the relationship fade between the two people and the differences come into sharper focus. More of an 'I' mentality arises, than a 'we' mentality.
This stage has to do with communication predominantly. Essentially, the two people start avoiding subjects that cause conflict (usually due to the differentiation from stage one). Within the relationship, each person sets up their own 'space', be it hobbies or activities, or actual physical locations, in which the other person might not be welcome.
In this stage, the negative patterns established in the last two stages become set. They aren't addressed, they aren't fixed and they become a part of the relationship. The separation is complete, it's just that the relationship hasn't formally been ended yet.
Since the people are now basically stuck in a pattern of not doing things together, they begin to actively ignore one another. Physically, they prefer to spend time alone. Mentally, they avoid spending time addressing the other person's needs. This is when they stop arguing and start simply avoiding the conflicts all together. It's the brink.
Almost doesn't bear explaining. One or both formally ends the relationship and that's that.
Interestingly, many platonic relationships never make it to termination. Avoidance is a more common stage to remain in. People will avoid the potential of formally ending the relationship. Or perhaps it's a fear of missing out if you ever want to rekindle things. Obviously however, with romances, it's a little harder to let things stagnate on and on (that's called empty love, it's a thing and it's very sad).
Fades the moonlight golden-pale,
And the bird has ceased to sing—
Ah, it was no nightengale,
But my heart—remembering.
- Excerpt - The Nightingale - Victor J. Daley