A number of factors likely influence this.
Corn is an annual. A new plant grows from seed every year, produces new seed, and dies. The seeds of the corn plant are the kernels on the ear it produces. Potentially, each kernel can produce a new corn plant.
Many modern corn varieties are selected for productivity under certain conditions.
- Herbicide applications reduce competing plants.
- Insecticide applications reduce the impact of damaging insects.
- Fungicide applications reduce the damage done by fungus.
- Irrigation provides the ample water required for corn to produce mature ears.
- Fertilization provides the nitrogen required for the significant growth that takes place each season.
- Tillage provides a uniform, receptive seed bed (or seed is "drilled" into the ground in no-till systems) and contributes to suppression of competing plants.
- Other human activities exclude larger pests (mammals, birds, etc).
So modern corn varieties growing without human intervention face a number of challenges. In its favor, a single plant can produce a significant number of seeds (assuming it can bring them to maturity) - around 800. Somewhat counterbalancing this, modern corn varieties are not particularly successful at self re-seeding. Further, seed from modern corn varieties is kept in dark, dry storage away from the fields where it cannot germinate and grow.
So, first, if humans disappear outside of the growing season then what is left behind is not a corn field but an empty field (or perhaps a field sown with some cover crop). Depending on where in the world the field is, this means there is perhaps a 50% chance that there will simply be no corn fields that can perpetuate and the answer to the question is that there will be no corn crop in any subsequent year. However, since the growing seasons are out of phase in the northern and southern hemisphere and corn is grown in both, another way of looking at this is that you will lose all of at least one hemisphere's corn fields. I'll naively consider this to be 50% and I'll call this "seasonal failure".
Then you have loses due to competition, predation, fungal infection, lack of fertility, drought, and reseeding failure.
So how much corn can you expect in untended fields?
× reseeding failure
× drought loss
× fertility loss
× fungal loss
× predation loss
× competition loss
= annual seed loss proportion
seeds per plant
× annual seed loss proportion
= annual population growth rate
Clearly each of these parameters has a different value depending on site, local conditions, and yearly variations. This gives you a framework to start making estimates, though, and perhaps answer the question for a particular site (eg what is the average annual rainfall in the particular area you're interested in? how does this compare with the water a field receives under irrigation. etc).
We can play with estimates for these values to get some sense of scale, perhaps. For example, I would guess competition, predation, fungal loss, drought loss, and seasonal failure at 50% and reseeding failure and fertility loss at 90%. This produces a result of 800 * (0.55 × 0.12) ≈ 0.25.
This suggests that, on average, for every 4 corn plants in a field, you'll get 1 corn plant in the next generation. At this rate, in the 3rd season you have around 1% as many corn plants as you started with. At some point, a non-linear factor of pollination failure creeps in (corn plants really like to be bumping right up against their neighbor for successful pollination) and you probably get a much more dramatic falloff.
Keep in mind I've just made up some numbers for these different kinds of losses. This may or may not bear any resemblance to any particular real world scenario. I suspect better estimates are possible for fertility loss but the other factors probably vary quite wildly from case to case. For example, you may see areas with no drought loss at all for many years at the same time other sites have complete loss due to drought.