Most car-following models show a transition from laminar to "congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the laminar into the congested phase. In stochastic models, one would intuitively assume that the size of this amplitude gets translated into a waiting time, i.e. until fluctuations sufficiently add up to trigger the transition. A recently introduced model of traffic flow however does not show this behavior: in the density regime where the jam solution co-exists with the high-flow state, the strong intrinsic stochasticity of the model is not sufficient to cause a transition into the jammed regime. Similar to deterministic models, a large external disturbance is needed to trigger the transition.