We investigated a series of telechelic polyisobutylenes, previously shown to exhibit self-healing, by means of small-angle X-ray scattering and rheology. All samples form a dense, dynamic network of interconnected micelles resulting from aggregation of the functional groups and leading to viscoelastic behavior. The dynamic character of this network manifests itself in the appearance of terminal flow at long time scales. While the elastic properties are distinctly molecular weight dependent, the terminal relaxation time is controlled by the functional end groups. The yielding properties under large deformation during startup shear experiments can be understood by a model of stress activation of the dynamic bonds. Stress relaxation experiments help to separate the nonlinear response into two contributions: a fast collapse of the network and a slow relaxation, happening on the time scale of the terminal relaxation. The latter is also known to control self-healing of the collapsed structure.