I think there is a limit to the amount that the difficulty can increase at each step.
The more the bitcoin network grows, the less likely it is to have large spikes in difficulty. The likelihood of a jump of that magnitude from a single entity is very unlikely. If that kind of jump does occur, it will more likely be from a large interested demographic discovering Bitcoin all at once, such as if it was featured in a major magazine. Bitcoin will cope with such increases and subsequent decreases just fine.
There is a limit to the difficulty adjustment, but for upward adjustments it is 300% (factor of 4 between new and old) rather than the 20% in my scenario, so it wouldn't help.
I would argue that a 20% difficulty adjustment is in no sense extreme - the last five adjustments were 44%, 35%, 300%, 93%, and 21%. This hasn't been a problem up to now, but obviously not because a 20% adjustment would be too extreme, but more likely because it hasn't been enough to make minting unprofitable (or otherwise uninteresting). My scenario does not assume that a single entity is responsible for a jump in difficulty - it is just as problematic if e.g. publicity makes minting 20% more popular at a time when the profit margin is less than 20%. The extreme effects come from the proportion of minters who are unwilling to continue minting at a loss. If this proportion is large while the profit margin is low, the system becomes very unstable.
Also, if I am right about the 4-year halving of bitcoins generated (i.e. that it
doesn't affect the difficulty adjustment) such events alone would be equivalent to a 100% upward difficulty adjustment. And it seems very reasonable to assume that most minters will have a lower profit margin than 100% in the future.