When I look at the "daily" jobs I have scheduled to run, they show to be set the way you are describing, with "every week day" selected, however, my job runs one time, every day.
Being unsure if the job is defaulting that setting back to "every week day", after you save it on "Every X Days", you could do an "advanced" schedule type, and then use the following settings.
Minutes: 00
Hours: 00
Day of Month: *
Month: *
Day of Week: *
That would run your job every day, of every week, of every month, at midnight.
Let us know what you find, please.
-Will