I've run into that also. In the web app, a banner pops up at the top of the page stating that the date has changed for that task. Part of that banner is a link to the task. Once you change it and it disappears from your Smart List, you can click that link to go right to that task.

Also, if that happens when you change the due date, try changing the start date first. Does it stay in place then? That would depend on how your Smart List is set up.

One more thought...
Is your task irregular regarding the dates? Or is it predictable? If it's predictable (same day or date every month, same day every week, etc), then the repeat pattern should change those dates for you.
Example: If it's due on the 3rd of every month and you have the start and due dates set to the 3rd, and the repeat is "monthly on the 3rd" then it should automatically advance the due and start dates to the 3rd of next month when it's completed this month. Does that make sense?