The Rotten Egg Nebula has at its core a binary composed of a Mira star and an A-type companion at a separation >10 au. It has been hypothesized to have formed by strong binary interactions between the Mira and a companion in an eccentric orbit during periastron passage ~800 years ago. We have performed hydrodynamic simulations of an asymptotic giant branch star interacting with companions with a range of masses in orbits with a range of initial eccentricities and periastron separations. For reasonable values of the eccentricity, we find that Roche lobe overflow can take place only if the periods are <<100 years. Moreover, mass transfer causes the system to enter a common envelope phase within several orbits. Since the central star of the Rotten Egg nebula is an AGB star, we conclude that such a common envelope phase must have lead to a merger, so the observed companion must have been a tertiary companion of a binary that merged at the time of nebula ejection. Based on the mass and timescale of the simulated disc formed around the companion before the common envelope phase, we analytically estimate the properties of jets that could be launched. Allowing for super-Eddington accretion rates, we find that jets similar to those observed are plausible, provided that the putative lost companion was relatively massive.