With technological advancements, you always have access to your work and contacts, making it difficult to be offline even when you are not physically present in the office. However, it sometimes becomes a necessity to step away and treat yourself to a vacation.
See, in my head, “as soon as possible” reads simply as a more formal way of saying “I will respond at my earliest convenience.” Like, either way, this person is getting back to you as soon as they can, whatever that actually means.

I received one from a coworker in middle management that said something to the effect of “I’m working on a large-scale project and will be unable to answer email until X date. Please contact [direct report’s email] with any questions.” This went on for well over a month.
Then there was the occasional one who would do what Alison mentioned with the sickness excuses, and create a tale that read like a police report: “I must miss my deadline because, on the night of August 12, my 45-year-old sister was alone in her house when an intruder entered. He was a 6’1″ caucasian male wearing a black balaclava and carrying a candlestick. As my sister approached him, with the dog barking around her heels, she heard a distant car crash which led her to have a fatal … etc.” (This is not an actual excuse I received, just similar in detail to some of those that were submitted.) These ones I was pretty sure were a writing exercise, requiring time and effort that could have been put to better use on the actual assignment they had been given.