How long should someone with respiratory failure be given 2liters prn oxygen. Each time the person either appears to be in distress or their 02 saturation levels fall

Depends. Most likely its not enough oxygen to compensate for the resp failure. There are some cases where someone who has severe COPD and the o2 may suppress respirations because in these people the elevated co2 is not what drives respirations since they live at such high levels. Most likely your are describing someone who needs an o2 mask or a breathing tube to get the o2 to the tissues/brain/heart.
What . What i tell my patients is to invest money in a pulse oximeter ( costs about 35-50$ online or cvs/costco/sams/walgreens etc etc) . Lack of oxygen with exertion or at night is dangerous and a strain on vital organs of our body. O2 saturations above 88% are desired with exertion at rest or at night. I am not sure of her history so i would recommend you to discuss this issue with primary care physician or pt`s pulmonologist.