New data of shear startup on branched styrene-butadiene random (SBR) copolymers are reported, where the novelty consists in repeating the startup run after different rest times at zero stress. Here, the aim is one of exploring the "damage" introduced by the first run, as well as the subsequent recovery, if any, upon waiting increasingly long times. Differently from a linear sample, our branched melts show multiple peaks during the first run, as previously reported by Bacchelli [Kautschuk Gummi Kunststoffe 61, 188-191 (2008)] for similar SBR samples, and, more recently, by Snijkers et al. [ACS Macro Lett. 2, 601-604 (2013)] for a well-characterized comblike polystyrene melt. The repeated runs show an intriguing novel feature with respect to the case of linear polymers, namely, the first peak goes up initially, instead of down. The second peak goes down and seemingly recovers only after an extremely long time, longer than the largest relaxation time practically accessible to linear viscoelasticity, the latter not reaching the terminal behavior. All such features of nonlinear viscoelasticity of highly branched polymers are interpreted by using a simple theory inspired by the well-known pompom model. (C) 2014 The Society of Rheology.