This is a new feature added in Love Plus+. After the 5th rank, you and your girlfriend can occasionally get sick. When this happens, all dating activity gets halted. Instead, you get the home visit events.
The Girl Gets Sick[]
When your girlfriend gets sick, you lose the options to email her, to call her, to ask her out, or to interact with her in Love Plus Mode. She does not go to school and will not visit during activities. She would be home, resting.
The event is usually signaled by her calling you in the morning telling you that she is sick. Although it is possible for see it before the phone call if you visit her the night before in the Love Plus Mode and discover her lying with an ice bag on her forehead.
Once she is sick, it takes about a week for her to recover. Visiting her daily is supposed to shorten the duration. You will get 2 emails from her after each visit, one to thank you, which you cannot reply, and another to tell you her condition, to which you get to reply with "Take care" or "Are you okay?". At the end of her illness, you will get a "I am feeling better" email. After that, you can expect a forced event the next morning where a healed Manaka/Rinko/Nene is waiting for you on your way to school and will be asking for a kiss.
When playing in Real-Time Mode it is possible to switch to Skip Mode and skip through the whole process. Note that the girl is not considered recovered until you have seen the forced morning event.