«Тысяча», as well as «сотня», «дюжина» (not very Russian), «пара» and, probably, some other quantity words, become a part of an adverb (= adverbial modifier of frequency in a sentence), and should be memorized as one adverb or as a SET EXPRESSION, e.g. тысячу раз, сотню раз, пару раз, дюжину раз. But only when this collocation equals to an adverb!