I'm looking for a manga where the main characters were lovers in the past but something happened/ the relationship didn't work out quite well. They would go their separate ways but then suddenly meet again and start falling for each other all over again.

I prefer the separation to be long for them to kind of have a change of character or somthing like that, although I wouldn't really mind it if it was shorter or if they didn't change at all.

I don't mind yaoi/yuri/shoujo ai/shounen ai

I don't think I have ever read a manga like this so I can't really give an example.
Thank you in advance!

Boku to Watashi no Henai Jijou - I don't remember the exact circumstances here, but it's definitely about two characters breaking up and the story of how they get together again.

For BL there's:
Hatsukoi no Atosaki
Taka ga Fukuen
Josou Danshi to Menhera Oji-san
Umibe no Étranger
Complex
J no Subete
Escape Journey
Kowagaranai de, Soba ni Ite, kind of.
Nigai no Theme, but only in the last chapter.
This Ending
Kyuuso wa Cheese no Yume o Miru and its sequel.
Hageshii Ame
Puchitto Hajiketa,

For GL:
Ohana Holoholo, maybe, but it's not completely scanlated and people say there's a chance that the new love interest will win instead of the old one, so...
Octave
Kaikou Effect

I think there're actually a lot of other titles like this, so a category search might help. Tags like "Reconciled Couple," "Breakup/s," "Reunited Lovers" etc., sound promising.

Complex
Sunadokei
Deep Flower

"The world is a dangerous place to live, not because of the people who are evil, but because of the people who don't do anything about it." - Albert Einstein

Ao Haru Ride
Masamune-kun no Revenge