Roadlocker said:
I actually had to go through the entire manga, look at the dates that are available and build myself a proper timeline and it actually is a whole 7+ months of separation from chapter 35 to 36, although we are not shown exactly when Mei goes away. She just leaves at some point after the wedding dress show in August.
Rough timeline of entire manga so far is like this:
School Year 1:
Before August: Mei's dad and Yuzu's mother meet and she agrees to do a paper marriage and take care of Mei.
August: Yuzu arrives at Aihara High after summer holiday in middle of a school year.
November: Mei and Yuzu go to grave of Yuzu's father and finally start connecting properly.
December: Mei and Matsuri have their shadow games and Yuzu does not dare to enter a relationship with Mei at this point. Mei cuts Yuzu off almost completely due to being angry and disappointed over the rejection, spends a lot of time working at school and pretty much just sleeps when she's home.
January: Mei is still giving Yuzu the cold shoulder.
February: Matsuri stops at Yuzu's house and asks how things are going with Mei. Yuzu is starting to despair.
Late March / Early April: School trip to Kyoto. Mei and Yuzu meet Sara and Nina. Yuzu manages to finally confess to Mei and realizes that Mei also needed her like this and not just as a step-sister. They start dating.
School Year 2 (Starting early in April):
April/May/June/July/August: Yuzu and Mei deepen their bond as lovers slowly but surely and Mei is feeling happier than she ever has in her entire life, but finally she can no longer bear the idea of marrying someone and forcing Yuzu to be her closeted lover at same time, because she becomes convinced that Yuzu wants open and true relationship based on her giving Mei an engagement ring and joking about matching wedding dresses.
She decides to put an end to it because she does not see a way to be with Yuzu openly and at the same time operating the business without marrying. In Japan there is a custom where eldest daughter is often married due to business interests in family if she is the oldest child. Husband is usually someone with business experience. This is just such a case. If this is not done, the family may face severe consequences in terms of losing face or their business suffering.
It might even turn into a scandal in the worst case. This is why Mei can't tolerate the thought of Yuzu getting torn apart in public. Mei likely believes Yuzu to be very fragile even against low key discrimination based on what she sees during summer. Mei also has a martyr complex thanks to her father and habits of high society that have rubbed on her, so she is naturally predisposed to act like this.
- Also, this is a confirmation of Mei's genuine desire to succeed the academy. If she was not properly committed on doing this, she COULD opt to be disowned from her family and maybe get adopted to some other koseki to free herself from the responsibility of marrying as is customary. This would then allow her Grandfather not only to adopt her intended fiance to the family through adult adoption, but also select him a bride outside his own family while maintaining the Aihara name on the business.
September/October/November/December: Mei and Yuzu are not together. - Still to be confirmed in manga.
School year 3:
January/February/March: Mei and Yuzu are not together. - Still to be confirmed in manga.
April: Yuzu starts her 3rd year in Aihara High with Harumin. Matsuri enrolls in as 1st year as well. Sakura is blooming. Most perceptive of Yuzu's friends and her mother can see through her happy act (Ume, Matsuri and Shirapon) and know that she is suffering deep inside.
Sorry about messing it up first. I got confused about the dates and such, since the two time skips in manga are quite abrupt and if you are not sensitive enough to the cultural and local context one can get mixed up on some things.