This is one of those "mechanics of ancient combat" questions which tends to be mired in debate due to the fact that most primary sources really don't go into much detail on the subject. They were writing for readers who already knew what contemporary combat was like so most of them didn't really see the need to.

That said there are a couple of reasons that archers might not use all of their arrows before engaging. The first may have been to preserve their strength. Repeatedly pulling a 100-150 lb warbow is extremely difficult, and one of Humfrey Barwick's complaints about archers in the late 16th century was that they tended to grow tired during combat and stop drawing their arrows all the way back. This problem was compounded if the archer had to spend a lot of time "roughing it" while on the campaign trail. Second, archers may just not have had enough time to shoot many arrows before one or both sides charged into melee. Not every archer in the army may have been capable of shooting at maximum range, especially with heavy war arrows, and those that could may have preferred to shoot at close range anyways where their shots would be more accurate and powerful. Messire Blaize de Montluc described encounters with English archers shortly before the Mary Rose sank and noted that they tended to shoot at very short ranges, at one point he writes that they closed to within "4 or 5 pike lengths" before shooting a shower of arrows.