Two things to remember:
1) dont cross open ground when the enemy has heavy machine guns in the vincinity
2) learn the difference between the various types of unit movement, and use them.
If you absolutely must cross open ground under fire, do so using advance or assault. These two stances will get your men exhausted within minutes though, and exhausted men are more prone to the panic sneak you are talking about. Advance is where the troops make short sprints from cover to cover, while they are laying down covering fire too. Just like the normal fire and movement tactic all armies use these days.
Assault is something you use the last 50 meters when you want to close in with the enemy. Think of it as a bayonets fixed, guns blazing charge.
Both these increase fatigue alot. Both also gives some positive modifiers for morale.
If you are not moving under fire, use move to contact, or move
Move to contact is normal move, but the unit will immideately stop upoin spotting an enemy unit or coming under fire.
Move is a relaxed move, think weapons on the shoulder, walking causally.
Both those stances reduce fatigue, but if a unit takes fire while in that stance, they tend to react more strongly (they freak).
Run is something you should not do unless you really really have to.
Basically those units are just running, they cant see toejam, they take enormous damage if fired upon, and they get exhausted very quick.
Sneak is...well sneak really. Beware of that command though, a unit will go from rested to exhausted in 20 meters using the sneak command.
