Them Yankees sure do like to run.
"Give them the cold steel, boys!" (Lewis Armistead)
[Note: routed units have their defending strength divided by four. Don't tell the Union Members, LOL.]
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Seriously though, it could be, and probably is, due to a range of things.
You say you are using 'default rules' and I assume this means that you have Rout Limiting checked. Although I would prefer, in the interests of realism, to have it unchecked, no-one else seems to want that and I have only ever played one game with that Optional Rule unchecked.
Once the possibility of that rule is eliminated it must be other things. Units rout because they have failed their Morale Check. Often the Union has more men but lower quality units although I have played scenarios where exactly the opposite is the case.
Look up the Manual and you'll see there are a lot of factors that modify the probability of a unit passing/failing its morale check. Presumably, as less of your units are routing, you are maximising the positive factors and minimising the negative ones. Your Union opponent is not doing as well in that regard and if his units are of lower quality that is having a greater affect. Plus, having more units will make will mean more units (in raw numbers) are routing. However, as a percentage of the force it is not necessarily so. [E.g. If the USA has 40 units and 8 rout then that is 20% of his units. If the CSA has 20 units and only four rout then that is still 20% of the units.]
There are tactical methods than can be used to increase the likelihood of an enemy unit routing but I'm not going to divulge that here. No, definitely not.
The Confederacy should win more battles and the Yankees should run. That is, to me, the natural order of things. [Although there is always the unexpected, isn't there?]