In order to improve the user’s experience, we decided to remove the profiles after you have Liked or sent a FlashNote to another user. You can see those profiles again in your Timeline if you cross paths with them again.
Moreover, it is not because a profile disappears from the Timeline that yours will also disappear from other users’ Timelines, as opposed to the cross button.
You can find a list of the users you sent a FlashNote to in the “Favorites” tab, under “My account”.