The compound word burnout is either a noun or an adjective. As a noun it refers to (1) a failure of something to keep burning, (2) physical or emotional exhaustion, (3) a fire that completely destroys something, and (4) someone whose mental faculties are diminished due to extended drug use. Its rare adjectival senses extend from its uses as a noun. When you need a verb meaning (1) to fail to keep burning, (2) to burn completely,or (3) to become physically or emotionally exhausted, use the two-word phrasal verb burn out.
Some publications hyphenate the one-word form—burn-out—in all or some of its noun and adjectival uses.
Examples
In these examples burnout is a noun:
Crews from Miami-Dade Fire Rescue and the state forestry division fought the fire with controlled burnouts and two water-dropping helicopter. [Miami Herald]
She argued she had been suffering chronic depression and burnout, which had since been treated. [News.com.au]
In the spring of 1976, David Bowie was dangerously close to burnout from fame and drugs. [Guardian]
And these writers correctly use the two-word burn out as a verb:
He’s brought in extra staff so as not to burn out his regular employees. [Province]
Billions of years from now the sun will burn out and leave the earth an uninhabitable cinder. [Wall Street Journal]
Crews intentionally started a series of fires in New Mexico trying to burn out potential fuel in front of the approaching blaze. [Daily Mail]