My guess is, when not doing anything, recent events morale bonus should tend toward 0.
If you just took a serious beating and barely escaped, the men should probably be happy you are not leading them into anymore battles for some time.
If you just plundered and slaughtered a lot, initial euphory will fade away, of course, but probably not to the point where they would desert en masse.
All of this assuming you keep the men fed and paid, of course.
The morale constantly going low would be ok if you didn't have to pay your men, that is, if they only had a share of battle loot, then they would have a reason for wanting to be in battle often (and winning of course).