A bear market is defined by the movements in the price index. All the A-D line is saying is that a few stocks were driving the market up, but most stocks were in fact losing ground. This is potentially unstable, but it can take some time before it becomes fatal, as we saw.
The fall from 1987 is also suspect because the A-D line has a downward bias. However, the fall from the late 1990s is too pronounced to be just downward bias.