Differential Amplifier constant output voltage
Refer to the Datasheet - page 5, table titled "recommended operating conditions".
The minimum supply voltage is +-4V - that's not 'approximately 4V', it's +4V and -4V (so 8V in total).  

Then refer to the datasheet again - page 6, look for "Common-mode input voltage range", and you'll see it's typical values are -13V to +13V with a +-15V supply.
So now you know the input voltage isn't allowed any closer than 2V to either supply rail.  

You need to either choose a different opamp, or increase your supply voltage significantly.