Similar to what others are suggesting:

Month-to-month doesn't work.

Mint's budget breakdown totally fails if my Landlord cashes my check too early/late.

Month-to-month doesn't work for expenses that aren't monthly. Example: travel.

Month-to-month doesn't work when the calendar lines up and you get 3 paychecks that month instead of the normal 2.

I'd be curious for a budgeting app that still has the concept of a month, but isn't locked to calendar dates.

Rolling average? Bucketed allotments that roll over? Maybe