In my experience, they can go away for long periods but flare up once in a while.
I've been sober a while now, and I think it was around the 5 or 6 month mark that I realized I wasn't feeling cravings anymore.
But I still get them occasionally, but they're much shorter, fleeting, and easier to dismiss.
In rehab, they kept telling is this phrase, "I want to use means I want to change the way I feel" which meant that when I had a craving I had to dig in and figure out what was really behind the craving.
I don't know if you've ever heard of the acronym HALT - Hungry, Angry, Lonely, Tired, but a lot of times cravings can be tied back to one of these feelings, so when a craving hits it's worth asking, when's the last time I ate etc.
Finally, if alcohol is your problem supplement, there are anti-craving medications that can be prescribed. There's Naltrexone, Campral, or off label use Gabapentin, which I understand can also be useful in marijuana withdrawal. They might be worth discussing with your Dr.
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"I danced in the morning when the world was begun. I danced in the moon and the stars and the sun". From my favourite hymn.
"If you see the wonder in a fairy tale, you can take the future even if you fail." Abba