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On the day a task starts, if you won't finish it, bump the start date to the next day. That way it will continue to be visible in the Forecast view the next day. There is a problem with this approach in that if the action in question is a repeating action, the dates for the next one will be altered. If you do this to a repeating action, you might make a note in the action title or note to remind yourself to put the next one right when you complete the current one.

Another approach would be to use a perspective that groups by start date, which would show you those items which have started but are not yet complete. Without a Mac, you'll have to contact the Omni support stff for their assistance in creating such a perspective.

Also on the Mac, I wrote a script which allows rescheduling the current event for a repeating task without disturbing future ones, but that isn't any use if you only have the iPad version of OmniFocus.

I use all of these approaches, but I tend not to adjust the dates on any but the most important as Forecast view would be hopelessly clogged with actions that could be started I use start dates primarily to indicate that it is not possible or desirable to work on a task before the start date, not so much to schedule myself to work that task at a given date/time.