Exhaustion recovers at a rate of 1/minute of rest, so it doesn't inherently cover the idea of weariness from prolonged difficult conditions. But you could apply a penalty on exhaustion checks which would result in characters becoming exhausted more quickly. This is how extreme temperatures, altitude, hunger, and lack of sleep are handled. It seems reasonable that this could also reflect being overwhelmed, depressed, etc.
If you take a look at the RMU Arms & Character Law beta, the fatigue/exhaustion rules start on page 18.