We live in a society where many people are consistently tired. Some go for days (or longer) on auto-pilot, sleep-walking from responsibility to responsibility to release. We are advised to not only eat better and exercise regularly, but to get enough sleep.
It may sound contradictory, but I think the admonition to get enough sleep corresponds well to Jesus' and Paul's command to stay awake.
What prevents a healthy amount of sleep? Stress. Worry. Chasing after things (or people). Fear. Chemicals. Pressure. Overusing our bodies and minds. Under-using our bodies and minds.
There are surely other causes, but some portion of our society's inability to sleep is self-imposed.
When we pray with a former Pope, "It's your world, God, I'm going to bed" (a sign we trust God to be at work in it) or we expend our time and energy in activities that contribute to God's kingdom coming (joining God at work in it) or come to a place of peace with what we have and who we are in Christ, we sleep better.
In this sense, being awake in Christ contributes to being able to rest well in him. The bridesmaids in Jesus' parable who were awakened to have what they needed could rest in him, even as they waited for the groom to arrive.
In the days between the dawning of Christ's kingdom and its final consummation, our ability to rest in him may be an indication of how awake in him we are.
Rest in Jesus, not from him.