The phrase "constantly craving" is correct and usable in written English.
It can be used to describe a persistent desire or longing for something.
Example: "She found herself constantly craving chocolate, even after a large meal."
Alternatives: "perpetually desiring" or "always yearning".
A democratic society is always in flux, debating and defining its priorities and challenges, constantly craving new achievements.
(The child in an alcoholic household with an abusive stepfather, constantly playing peacemaker, constantly craving affection. It doesn't take Freud...) But housing two radically different lives between one set of covers makes a deeper sense.
This isn't even counting the other brain changes, such as how connections with the frontal cortex and other cognitive processes actually scramble conscious control and motivation, so people are constantly craving and seeking out the drug, despite copious evidence for the terrible damage it's wreaking.
During every shift, they see an America that is constantly craving, yet they're overlooked.
When you're in that place -- where I have been before with 'Requiem [for a Dream]' -- you're constantly craving.
The feeding frenzy mentality that turns someone into the subject of instantaneous media fascination and public gawking leaves the herd constantly craving fresh meat to feed on.
They constantly crave more.
From my little window, I could smell pommes frites wafting up, so I constantly craved them.
And so we lurch from site to site, if only because we constantly crave the fleeting pleasure of new information.
Angela Scotchel, overwhelmed by anxiety about her future, constantly craved and sometimes gave in to her desire for Xanax.
In online advertising, we constantly crave the attention of that dynamic and yet all too often elusive demographic group: millennials.
