There is ongoing debate over whether Arctic sea-ice has already passed a `tipping point, or whether it will do so in the future. Several recent studies argue that the loss of summer sea ice does not involve an irreversible bifurcation, because it is highly reversible in models. However, a broader definition of a `tipping point also includes other abrupt, non-linear changes that are neither bifurcations nor necessarily irreversible. Examination of satellite data for Arctic sea-ice area reveals an abrupt increase in the amplitude of seasonal variability in 2007 that has persisted since then. We identified this abrupt transition using recently developed methods that can detect multi-modality in time-series data and sometimes forewarn of bifurcations. When removing the mean seasonal cycle (up to 2008) from the satellite data, the residual sea-ice fluctuations switch from uni-modal to multi-modal behaviour around 2007. We originally interpreted this as a bifurcation in which a new lower ice cover attractor appears in deseasonalised fluctuations and is sampled in every summer-autumn from 2007 onwards. However, this interpretation is clearly sensitive to how the seasonal cycle is removed from the raw data, and to the presence of continental land masses restricting winter-spring ice fluctuations. Furthermore, there was no robust early warning signal of critical slowing down prior to the hypothesized bifurcation. Early warning indicators do however show destabilization of the summer-autumn sea-ice cover since 2007. Thus, the bifurcation hypothesis lacks consistent support, but there was an abrupt and persistent increase in the amplitude of the seasonal cycle of Arctic sea-ice cover in 2007, which we describe as a (non-bifurcation) `tipping point. Our statistical methods detect this `tipping point and its time of onset.