The usual cause is a bug in Word 2007 that prevents date autocomplete from
happening if the zoom is set "too high". It's not clear what "too high" is,
though. I keep mine at 160% most of the time, and date AutoComplete does not
work. If I set it back to 145%, it works. At 150%, it works sometimes, but
not usually.
Here, I've never seen AutoComplete fail if the zoom is set to 145% or
lower... and I've never see AutoComplete work if the zoom is set to 160% or
higher. Between 145% and 160% seems to be a Twilight zone of sorts.