Here's my 2 cents for what it's worth ...

Midnight is a single point in time. Seconds, minutes, hours, and so forth are time ranges, not single points in time, so you're trying to compare apples to oranges.

Or in other words ...

Midnight is exactly 12:00am, a single point in time, not 12:00:01, not 12:00:01.0000001, not 11:59:59, etc ... The "last second of the day" is a time range of one second in length, not a single point in time, just like "the last hour of the day" is not a single point in time, but rather a time range.

If a writing contest says it's due **AT** midnight, May 31, I would say the author exercised poor grammer, and probably has no business being involved in a writing contest of all things. How can you turn in your subission at exactly a single point in time? They probably should have worded it **BY** midnight, May 31.

That's my opinion and I'm sticking to it ;-)