Firstly, great plugin - very slick and I like it a lot.
I've worked around this problem, but just wanted to let you know in case it's an easy fix.
I installed the Questions plugin into a multisite installation then enabled it for the network. TheSurvey menu option appeared correctly in the sub-site, but when trying to save a new survey, it cleared the details and only a blank post was saved.
After enabling the debug log, I found that the following was being output ('multisite' is the db name):
[21-May-2015 14:46:08 UTC] WordPress database error Table '...multisite_21_questions_questions' doesn't exist for query INSERT INTO multisite_21_questions_questions
(questions_id
,question
,sort
,type
) VALUES ('294','','1','OneChoice') made by edit_post, wp_update_post, wp_insert_post, do_action('save_post'), call_user_func_array, Questions_Admin->save_survey, Questions_Admin->save_survey_postdata
So it appeared that the database wasn't being correctly initialised when the network enable was chosen. If I disable the plugin at the network level then enable on the site, it works fine.
Looks like an extra hook might be required for network enable, or the readme.txt updated to say that it should only be enabled at a site level.