The 'u' version lasted from Anglo-Saxon times until the late 1600s, when the 'dropped-u' version first appeared. The two forms existed then side by side for another century or so, before the 'forty' took over completely.
As to why, it was simply the tendency for language to simplify as time went on. In the same kind of process, 'the mannes house' became 'the man's house', for example.
I should perhaps have pointed out above that the word 'four' itself was generally spelt 'feower' in Old English times or some similar form suggesting that there was a definite 'ow' sound in there. As a matter of interest, 'four' is still pronounced that way in Scotland. The 'four' spelling appeared as early as 1300 AD, but was probably still pronounced 'fower'.