The duration of action is determined by how long the drug remains in the body. There are two ways for the drug to leave your body: it can be excreted (in the urine or feces mainly) or it can be metabolized into something else which is then excreted. More polar compounds are more easily excreted because they are more soluble in water, and the body thus does its best to metabolize lipophilic drugs into hydrophilic compounds instead, often by adding -OH groups.
If you want to extend the duration of action of a compound by synthesizing an analogue with the same pharmacology but which remains longer in the system, there are two main ways to do it: you can make it more difficult for the body to excrete the drug, or you can make it more difficult for the body to metabolize the drug.
The DOx drugs have a longer duration of action because they have a methyl group at the alpha position. This means that the drug can't just smack an -OH group onto this carbon, and thus it takes longer to metabolize and has a longer duration of action. You can see that DOC is 2C-C with an alpha-methyl, DOB is 2C-B with an alhpa-methyl and so on, which means that the DOx's all last 2-3 times longer than the corresponding 2C-x's.
The alpha-methyl is not making the molecule more polar - if it did, it would in fact be easier to excrete. It's making it a tiny bit less polar actually, since a methyl group is lipophilic, but the reason for the difference in duration of action is not due to changed lipophilicity - rather, as mentioned earlier, it makes it more difficult for the body to metabolize the drug. Increased lipophilicity also makes it easier for the compound to cross the blood-brain barrier, which means that it's active in lower doses - and as predicted, 2C-x's are used in 10+ mg doses while DOx's are used in doses closer to 1-2 mg.
