Three years later, and this is still happening to me!
Searched my Contacts app for a specific street name (looking for my neighbors), and after scrolling to the bottom of the search results, the last three are off the bottom of the screen. If I hold my finger on the screen and drag up, I can see them, but when I let go, they spring back down off the bottom of the screen, so I can't open them. I can find them other ways, but this is very maddening!
Using an iPhone 7 Plus. Many many contacts in my address book.
This does not happen, when I use the Contacts tab in the Phone app. That's a great workaround, but what the heck is going on with the contacts app?