Eye strain is generally not a direct results of stress, but rather a parallel symptom of the situation causing stress.
Historically not so long ago the most common job was toiling away in the field from dawn till dusk. That kind of work is simple but very exhausting, challenging the physique but not the mind. Today, the most common kind of job involves endlessly staring at a computer monitor or arching over a desk - even when it is not stressful, it requires a lot from our eyes.
What stress does is that it eliminates our sense of when we should take a break, even if only for a few minutes. Sometimes we even forget to blink. During the course of days or weeks of such work (or even longer) the damage to the eyes may become irrecuperable as we deny even the slightest moments of rest when our eyes need them most.
Flexibility of rest is important when dealing with stress related eye strain. It is not enough to have a good night's rest, but also to close your eyes and take a few breaths worth of time often during stressful work.