Overall, your corn plant looks reasonably well.  I think the three growing points make it an attractive plant and the leave color looks good in the photograph.  I can see that the dead leaves are clustered in the middle of the growing stem.  It leads me to think the young leaves growing at that time were affected my some growing condition. 
My first recommendation is to carefull cut out the dead tips and leaves.  You have indicated that the plant is not in direct sun, but gets some bright light.  Direct sunlight will burn the leaves.  Humidity around 50% and temperatures between 60 - 75F are best for these plants. Also keep your plant our of any draft from furnaces, air conditioners, and windows. Watering every 10-14 days may not be enough. The soil should be kept evenly moist, not letting it dry out. Try watering every 7 days if the soil is getting dry.  You can raise the humidity by placing the plant on a tray with some stones on it and water placed in the tray. Your plant may also do well with frequent misting.  You should need to water less in the winter.
It is natural for the lower leaves to dry up and die as they age.  Just cut them off when they become unsightly. 

I hope your plant recovers.