Check engine light shutting on and off intermittently?

I got my car listed above about a year ago, it had the check engine light on when I bought it. I was told it was the o2 sensor. We didn't change it at the time, and after a month or so it went off. A couple months ago it came back on, assuming it was the o2 sensor we left it alone and it eventually went off. A couple weeks ago it had come back on, this time I decided to get it checked. At AutoZone I got codes P0606 and P0137. After doing research on P0606, we got and changed the o2 sensor, and the check engine light went off after around 50 miles. The next day I get in it to take my kiddo to school, it's back on. I decided to take it to O'Reillys to get it checked there. I get code P0606 again. We start thinking it's the ECM/PCM, so we start looking into taking it to a dealership. (Which is not what I want to do) After a week or so it went off again. I think I'm in the clear but still confusing. This morning, I get in the car to take my kiddos to school. The light is back on, after a couple hours of sitting I get back in it to pick them up from school and it goes back off. What in the world would cause my check engine light to keep switching on and off? The o2 sensor was a cheaper on so I am going to try and better brand one. What else could be causing my check engine light to do this?