Organic radicals are neutral, purely organic molecules exhibiting an intrinsic magnetic moment due to the presence of an unpaired electron in the molecule in its ground state. This property, added to the low spin-orbit coupling and weak hyperfine interactions, make neutral organic radicals good candidates for molecular spintronics insofar as the radical character is stable in solid state electronic devices. Here we show that the paramagnetism of the polychlorotriphenylmethyl radical molecule in the form of a Kondo anomaly is preserved in two- and three-terminal solid-state devices, regardless of mechanical and electrostatic changes. Indeed, our results demonstrate that the Kondo anomaly is robust under electrodes displacement and changes of the electrostatic environment, pointing to a localized orbital in the radical as the source of magnetism. Strong support to this picture is provided by density functional calculations and measurements of the corresponding nonradical species. These results pave the way toward the use of all-organic neutral radical molecules in spintronics devices and open the door to further investigations into Kondo physics.