It's obvious that you're a veteran, Stephen -- you've got it nailed. "Cowardice under fire" is a term much beloved by generals and other fools to explain why a soldier or a regiment folds in combat. But those who "have been there" know that every man on the field at Prairie Grove was scared. What makes scared men do their duty is unit cohesion, faith in their leaders, and belief in the cause they're fighting for. Adams' regiment had none of these things.
The men of Adams' regiment were, for the most part, very reluctant conscripts from various counties in northern Arkansas. With the exception of Companies A and E, which were recruited from men who were neighbors and relatives, the other companies were made of men from different areas who were sort of thrown together on a more-or-less county basis. Most of the company officers were also conscripts who had been elected to their positions. With one exception, Lieutenant-Colonel Samuel Peel, the field officers were not known to the men. In the short four months between organization and the battle of Prairie Grove, there were many changes in the field officers, including three different colonels. General Hindman finally brought in Charles W. Adams as colonel, Colonel Fitzwilliams was reduced to lieutenant-colonel, and Peel was booted out. Not a good recipe for unit cohesion and trust between officers and men.
A small core of men, again mostly in Companies A and E, had rushed to join the Arkansas State Troops when the war started, and had fought at Wilson's Creek together. These men were mostly pro-Southern in attitude; but by far the majority of the men were either pro-Union or decidedly neutral and wanted absolutely nothing to do with the war. In other words, they were concripted to fight for a cause they didn't believe in. This attitude is expressed very well in the autobiography of Pleasant Houston Spears.
When you throw all these factors into the mix, it becomes very clear that the easy answer of "cowardice" falls far short of the truth in explaining what happened to Adams' regiment at Prairie Grove.
There are very few surviving documents from Adams' regiment. I've tracked down all that I know of. One of the documents I've transcribed is a post-battle payroll list of the men who rallied to the colors at Prairie Grove. It consists of 76 names, exclusive of field and staff officers. Interestingly, most of those men were veterans of the Arkansas State Troops and the battle of Wilson's Creek, many of them having served in Capt. Larkin Bunch's company in the 4th Regiment State Troops.
As to the "cowards", the overwhelming majority joined the Union army and subsequently fought in many savage engagements for the next three years -- not exactly the definition of men who only wanted to duck a fight.
This here Civil War business is a whole lot more complicated than the official reports would appear to indicate. That's one reason why many of us out here are eagerly awaiting Bill Shea's book.