The fact that missile units will "chase" routers is certainly annoying...but it's also not new. The only answer I have is to just keep paying attention, requires some micro-management. Personally, I'd like to see some sort of mechanic where a missile unit will not chase a routing target, but we don't currently have that.

One option is to simply not target individual enemy units at all. Simply turn on "fire-at-will" and let them shoot at whoever comes within their range. The obvious downside is that they may waste ammo on undesirable targets. But neither will they run off on a wild-goose chase.

Are your missile units' firing arcs visible on the field (I think that's a selectable option)? If not, and you're panned out a bit where you can't easily see the individual troops, then part of your problem may be that they're facing the wrong way. If they're in skirmish mode, then sometimes they about-face to run away....and then when they stop at a safe distance, they don't about-face again. They just stand there with their backs to the battle, and it's not necessarily obvious to you. So, I would suggest turning on the firing arc visibility; much easier to see if they're facing the right way. Also very useful during pre-battle maneuvering to see where your missile troops will engage at max firing range.

If we're talking specifically about infantry archers, then you might try this: Park them safely behind your melee line, and then turn skirmish-mode off. It won't solve the "chase targeted routers" problem, but will ensure that skirmishing behavior doesn't inadvertently leave them facing the wrong way. This technique doesn't work well with slingers or javelin troops, though, because those types are typically working ahead of or to the side of the melee line, rather than from behind it.