Conductive rubber nanocomposites were prepared by dispersing conductive nanotubes (CNT) in thermoreversibly cross-linked ethylene propylene rubbers grafted with furan groups (EPM-g-furan) rubbers. Their features were studied with a strong focus on conductive and mechanical properties relevant for strain-sensor applications. The Diels-Alder chemistry used for thermoreversible cross-linking allows for the preparation of fully recyclable, homogeneous, and conductive nanocomposites. CNT modified with compatible furan groups provided nanocomposites with a relatively large tensile strength and small elongation at break. High and low sensitivity deformation experiments of nanocomposites with 5 wt% CNT (at the percolation threshold) displayed an initially linear sensitivity to deformation. Notably, only fresh samples displayed a linear response of their electrical resistivity to deformations as the resistance variation collapsed already after one cycle of elongation. Notwithstanding this mediocre performance as a strain sensor, the advantages of using thermoreversible chemistry in a conductive rubber nanocomposite were highlighted by demonstrating crack-healing by welding due to the joule effect on the surface and the bulk of the material. This will open up new technological opportunities for the design of novel strain-sensors based on recyclable rubbers.