The phrase "insatiable urge" refers to a strong and unending desire or craving for something, which cannot be satisfied no matter how much you try. Full definition
Could everyone in this tiny town be experiencing the same insatiable urge? (holajalapeno.com)
From the pandemic of pornography to reality T.V., to the insatiable urge so many feel to make the whole of life a performance on Facebook and Twitter, the distinction upon which civilization has depended — a careful demarcation between the public and the private — is dissolving before our eyes. (firstthings.com)
At first smell of the fragrant melons at my local Ralph's I got an insatiable urge to throw a little backyard staycation to celebrate. (holajalapeno.com)