Here's the way I see it-
If the course wasn't an online course, and the professor gave you a 48-hour period during which you could come in to take a sit-down test, it'd be absurd to ask that period to be extended. I don't see why it should be any different for an online test.
If there are exceptional circumstances for why you cant take the test in any given 48-hour period, I'm sure your professor will accommodate you, but doesn't appear to be the case.