1. Do not allow to pull the bow while running - Archers will be faster due to lower encumbrance and are fast to reposition, but go through the shot motions when stationary. If infantry approach, archer can either stand and shoot, or run, but not an effective combination of both. The draw time (which I think should increase and traded for more damage per arrow, but is a whole other issue) is long enough to allow the infantry to close if the archer stops to shoot.
2. Equalize athletics - I agree that there is no reason to make archer inherently slower that infantry, but not faster either. They should be about equal and the typical added encumbrance of the infantry will make the difference. Not fast enough to flat out outrun the archer, but fast enough to corner him.
3. Under no circumstance make archer a pushover in melee - Archers have decent melee skills that should allow them, on roughly equal footing, to turn the player skill into the dominant factor. They do not have to instantly roll over and die if the infantry catches up - infantry players do not want to run after targets and kill them like baby seals, they want a melee fight damit! They chase a fighting opportunity, not a scoreboard kill.
The Khergits are a unique case - they have un-catchable archers, but at the same time, less lethal and less accurate when riding. I see many of them using the horse just for repositioning: move, stop, shoot, reposition. Against them infantry are of little use (maybe help vs. the lancers) and most people go cavalry or archer. I dislike fighting the Khergits for this reason, but it is variety.