What is the screen life of an Android Tablet? I'm unable to find technical specs on the life expectancy for the screen of a Nexus 7 (or any Android Tablet, for that matter). 

Do you know how many total hours we can expect to get out of a tablet before it starts to die out?

FYI: I'm considering to use an Android tablet as the touch screen for an Industrial Controller. The Industrial Controller will be turned on 24/7 - which is obviously not the typical use case for a tablet - so I'm concerned that the tablet will burn out too soon (i.e. within a year or two).
Sorry, this answer is slightly off-topic but still important for your use case.

The thing you are most likely to have to worry about is heat.  Having the screen on will generate heat, and you will need to plug into an external power source which when charging the battery will also generate a lot of heat.  This could damage the internal components (including the screen) over a long period, but unfortunately I don't have any evidence to support this.