Since I was able to find a computer which was the exact same version as the one I had in my car for a relatively cheap price, I though I would go that route first.
I snapped the old one out and put the new one in and then went to my mechanic to have all of the computers cleared/reset.
It seems to have solved my problem (at least temporarily). Normally the check engine light would come in the following day (with light driving). It's been off for 4 days now.
Should I have the same problem in the future, I'll replace it with a newer software revision as suggested by Mercedes Benz. Heck, I'll keep my eyes out for this newer computer to see if I can get one just as cheap.