"This book is not ending."
Translation:Bu kitap bitmiyor.
Subjects of tenses never take the accusative case. It is reserved only for the objects of verbs when they are specific. Some verbs (like sevmek) like to take the accusative almost always. Some time expressions also use the accusative.
There is sometimes some confusion in that the 3rd person possessive suffix and the accusative can look the same (on words that end in consonants). "kitabı" can mean "his/her/its book" or be "book" in the accusative case. However, like I said, subjects are never in the accusative case.
Simply put, subjects are always nominative, never accusative. Direct objects are sometimes accusative (when they are specific [i.e. I am reading the book "Kitabı okuyorum"] or after certain verbs). Direct objects are sometimes in the nominative case (when they are general [i.e. I am reading a book or I am reading books "Kitap okuyorum"]).
One more thing worth mentioning. If a noun with the 3rd person possessive suffix is a direct object, it is always specific and will always have the accusative on it. "Kitabını okuyorum" = I am reading his/her/its book. :)