OK, so my genset is 1991 vintage Onan 4BGE Emerald Plus. I had a similar issue and tried replacing a few parts but that method could get expensive quick. I took it out and took it to Cummins local repair facility. Turned out my issue was the generator's voltage regulator failing after it ran for a few minutes (less than 30 minutes). The part alone was nearly $300 in 2008 so probably more now. Total bill with labor was just over double that amount. Good news is no more issues and they could do the repair without replacing parts that did not need replaced.
I did a fair amount of research and did not get anything that would have led me to this part as the issue?!