To replicate, create a quiz and add multiple choice questions.
Then disable and uninstall quiz.
Reinstall quiz.
Between the uninstall and installl, do a db update to make sure.

The previously created quiz multi-choice questions are still in the database. And so are the previous quizes.
Go into the available quiz and then to manage questions. They are available but not yet added. Add the questions by checking the boxes and click submit.
The below error appears (with others) and nothing is added.

Notice: Undefined index: weights in quiz_questions_form_validate() (line 1418 of /sites/all/modules/quiz/quiz.admin.inc).
No questions were included.

Now click on one of the question and proceed to edit.
This time the error is:

Notice: Undefined property: stdClass::$choice_multi in MultichoiceQuestion->getDefaultAltSettings() (line 685 of /sites/all/modules/quiz/question_types/multichoice/multichoice.classes.inc).

The obvious reason for at least the first level is that while the uninstall does not remove the quiz question and quiz, it does remove the question Alternatives. So we end up with misconfigured questions at above attempts.

Now, during uninstall, warnings are given about leftover content. Problem is that this leftover content breaks quiz when you later re-install and attempt to create content.
Quiz should delete quiz, questions and alternatives on uninstall.