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Following a quench, colloidal systems with strong, short-ranged, attractive interactions can exhibit transient gelation, instead of the classical phase-ordering mechanisms of spinodal decomposition or nucleation. The particles aggregate into a tenuous, system-spanning network, which, for a time, remains robust to mechanical disturbance. Eventually, the network's ability to recover from destructive deformations becomes compromised, and the gel collapses. A detailed experimental study of gel collapse was reported in the preceding, companion article, leaving several open questions regarding the processes involved. We present a theoretical investigation into the factors affecting a gel's lifetime, concentrating in particular on the surprising influence of the size and shape of the container. We construct a model in which solvent dynamics are replaced by a dissipative coupling of the particulate network to a fixed frame and show that, in the absence of zero-frequency elasticity, such a coupling results in a novel class of matter in which stresses cannot propagate beyond a finite distance. We find our prediction of the characteristic length to be in quantitative agreement with the experimental data, and show how its ratio to the dimensions of the container controls the sedimentation. We discuss some aspects of the ageing mechanism, and suggest that a sudden collapse is ultimately due to erosion with positive feedback.