My testable hypothesis is that since the soils in the Sonoran Desert have pH that range from 7.0 to 8.0, neutral to alkaline pH, maybe the root aphids are adapted to higher pH, less acidic conditions. It could easily be tested without risking the plant by collecting some visibly infested soil in a clear cup, adding some pH adjusted water, say pH 5.5-6.0, letting it work for say one hour, then assess if the bugs were killed. If so, then it could be tested on a plant. After treatment for one hour, the container could be flushed with 7.0 water to remove the extra acid to achieve the desired final pH. Couldnt be any more traumatic than the methods tried by desertdan, much cheaper, and the downside is some browning on some leaves, not good but not necessarily lethal to the plant, According to the GWE tutorial concerning rapid pH fluctuations. If the problem is to be solved sometimes measures that could temporarily set the plant back should be considered. Pardon my scientific approach. Good luck! These root aphids are not a problem here in our sandy acidic soils. We deal with root knot nematodes here and they do the same root damage as the aphids. To combat them we use limestone or dolomite to raise the soil pH to around 6.5-6.8. Not sure if it kills the nematodes or causes them to flee the treated area but it does allow a crop to be harvested. Due to the tremendous buffering capacity of the acid sand soils, the limestone must be added every year before planting.