There's a couple of reasons why the covers don't change.
1. It's the person's internet or web browser. If the internet is unstable or is slow, it takes a few hours to a few days. A web browser could have something that booksie needs but doesn't have. Using a different internet or web browser could help. Web browsers that I know that works with booksie Firefox, Google Chrome, and Opera. There could be other web browsers that I'm not aware of that works with booksie.
2. Confused data/cover size. Data sometimes gets confused and doesn't work properly. The data knows that the cover was changed, but it takes a while for the data to preform a function. In some cases a photo size can also cause data to be confused like if the size is too big or too small for a function to preform.
3. It's booksie itself. There could be a miscommunication between servers and
data, it almost like confused data. The servers talk to one another by sending data; the data sent from your device told the booksie server that the cover is going to be changed and the data from server told the cover function to change the photo. While the data and the cover function are talking it's possible that the data or cover function got cut off resulting in a photo changing for some people while for others the photo remains the same.
Sorry for all the technical talk that may have confused you, I took technology classes in college and confused data and server talking are the subject the class teaches for coding.