Mail in this type of combat was very useful, but it was not long before pieces of plate armor began to be added at the elbows and knees and then to other areas of the body. This evolution spawned another and the arms race was on! One popular adaption was the increasing use of impact weapons like hammers, axes, maces, flails and clubs.
Through the inventive change in circumventing the better armor of the day (300100), the sword still remained the favored weapon. It signified honor, grace and skill, not like the bruising animal-like beating one could give with other weapons. Any one could swing a club or hammer, but it took a real soldier to wield a sword.
Another of the reasons for this was the fact that mail was fairly expensive and time consuming to make. Frequently it was the rich or one who had a rich patron who would be in possession of it.
Though the high classes had mail, the rank and file mostly did not. They were still innovative though and thought just as highly of preserving their skin. The basic protection consisted of heavy leather and or a gambeson and helm with perhaps some mail captured as spoils from a foe.
These things made the sword retain its high value on the battle field. Of course the horrendous capability against those lightly armed was pretty attractive attribute too!