Why is corn still left standing in the fall on farmer fields?

The reason why is that the Farmer who owns the crops is most likely waiting for the crop to dry down. This refers to moisture content of the grain. Depending on the grain, you would have to spend much more in money to "dry" the grain down in a storage bin. This is a costly process. They also do not harvest and store grain when the moisture is too high, this leads to mold and fungus growth.

Most of the time in the midwest, all of the crops are finished or harvested no later than mid-October. If crops still remain, its most likely do to inclement weather such as excessive rain which takes much longer to dry the grain and the fields until harvest can resume in cooler weather.