"Here" what we consider "the eroded areas" just do not have yield potential.  Their biggest shortage is soil depth, which equates to a shortage of water holding capacity, which is exacerbated by extremely low permeability meaning that when they get reasonable rain events during the growing season it runs off,  When they get extended rains which finally get to field capacity (usually out of season in our climate) they don't give up the moisture which they have very easily.  

Organic matter is a very good call....and it is the closest thing there is to a "fix"  because if you can get enough of it added it will help with all of the above problems.  N in any other form will only make it worse by building more plant when there is moisture, which depletes it even faster.  

Just my thoughts.....may not be even close to applicible to your situation.