The most likely guess if that the TV is broken. If it's under warranty get it taken care of by the seller or manufacturer. If you bought it with a credit card the warranty period may be extended by the credit card company. Diagnosing and fixing things today, unfortunately often costs more than buying a new TV, especially with bottom of the line TVs.
That said did you check if the TV has any programmable timers that have been started. Also find and cover with opaque tape the small window on the front of the TV that allows it to see the signal from the remote. This will rule out interfering inferred signals shutting the TV down.