  Oscillating solutions to the effective equations of Loop Quantum Cosmology
have been suggested for the role of an `eternal seed', providing a possible
starting point for the emergent universe scenario. We investigate the stability
of a particular model, sourced by a homogeneous massless scalar field and a
negative cosmological constant, with respect to small perturbations and to
quantum collapse. We find that the model has perturbatively stable and unstable
solutions, with both types of solutions occupying significant regions of the
parameter space. All solutions are unstable with respect to collapse by quantum
tunneling to zero size. We discuss the possibility that the state resulting
from the collapse is non-singular, so it may tunnel back to the oscillating
regime. We argue that the universe is then likely to evolve to states of very
large size with large particle occupation numbers.
