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I had the same issue and on the blog or in help somewhere found the solution.

Go to preferences / data and change "When entering due dates without times use..." to say 11:59 p.m.

On the same page, toggle "Make Actions due "soon" which are due in the next:.." to the 24 hour setting.

So it's Monday at 3 pm and you want to bump a task onto your perspective for tomorrow and get it off the screen right now. Change the due date to tomorrow's date, or type Tue, or type 1d in the date column, and that in effect makes the task due at 11:59 p.m. Tuesday, which is more than 24 hours from now, so it disappears from your perspective for now. I assume that it would reappear at 11:59 p.m. Monday, but I am usually in bed by then.