In 1995 I was on a business trip in Washington when we entered Daylight Savings time, but was on a different business trip in Arizona when we returned to Standard Time. Since Washington like 45.5 or 46.5 of the other states (at that time) observed Daylight Savings time, I dutifully moved my clock and adjusted my internal clock to the new time. However, Arizona didn't (and still doesn't) observe it, so when we left I had no clock to adjust. Thus the loss of an hour.
Of course my in-laws have reversed the process the last two or three years by heading down to Arizona in December and returning after March, so they get an hour back in October or November without having to save it in March.
Of course the best case of using time changes to your advantage was what my father and his coworkers did in the 1950s when they traveled to various parts of the South Pacific for bomb testing. The trick was to make sure you flew one way on a weekend so that you got two days credited as travel time (and overtime pay), but flew back so that you didn't loose any days on the way back. I cannot recall exactly how this worked out right now, but apparently it was quite common.