If you originally purchased a short-term rental, you will be prompted to purchase the book again if you try to access the book after the rental period expires.
If you purchased perpetual access -- or if your rental period has not yet expired -- and you are not seeing a book you previously purchased, you may have purchased it under another account.
If you originally created an account using an email address and password, and later log in using Facebook, Google, or Twitter, then Perusall will create a second account for you, and you won't have access to the courses or purchased books from your previous account. As a result, make sure you use the same method of signing in consistently -- e.g., if you originally signed in through Google, continue signing in through Google; if you originally created an account with an email address and password, continue signing in using that email address and password.
If you forget your password for an account you created using an email address and password, use the Forgot Password link on the login page to have a reset password link emailed to you.
If you are still having trouble accessing a book you purchased, contact Perusall Support.