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.
I understand what you are saying, and I am able to replicate it on my system too. I can definitely see how it is confusing, knowing what you picked, and seeing a different option by default when you go back into the job.
Being unsure if the job is actually defaulting that setting back to "every week day", after you save it on "Every X Days", or just showing you (which I think it is), 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.
An answer from one of the SolarWinders would probably be best, to clear things up...
Let us know what you find, please.
-Will