In particular people fear "burn-out" and they are right to: it can do great damage.
But having "the same attitude as that of Christ Jesus" will sometimes mean rest as well as activity. The man Jesus needed rest when he lived on this planet (Mark 6:31 & 46).
But its worth us changing our perspective on why such rest is needed. We treat it as human right. Something we've earned. Jesus seems to have used it as an opportunity to prepare for more self-sacrificial ministry (using it to pray); so that even his times of rest had self-sacrifice as their aim. We, as Don Carson points out, need to have the same attitude:
Many see vacations as the end or purpose of work, and even of life itself. Their work earns a holiday; they then deserve a vacation. When they return from their two or three weeks, they hate the thought of going back to work; and they can hardly wait for the next set of holidays. By contrast, the Christian loves to serve. Ministry of all kinds is the end, the purpose; holidays are simply a means to that end. Far from serving in order to earn a rest, we take rests now and then in order to serve the better.That's why we need to rest. So that we can be more self-sacrificial. Is that why you rest?