Ayesha has had several bugs regarding stuck LP. I would pursue the harem only after getting her storyline done if it is causing problems. I have done the harem, a week or two ago, but I dont remember if it did or didnt cause problems.
Viewing post in Love & Sex : Second Base comments
Was stuck there too.
To start the beach date: you need to be at 20 LP, on summer, weekend, between 14:00-16:00 o´clock, need to have atleast a bike and you have to call her on phone and ask for a date!
Her next date is quite specific too. You don't have to take her to a cinema date instead you have to meet her when shes at the cinema on her own and than there will be a new "invite to date"-icon for her.