Q:

What happens if hash rate decreases rapidly?

Since difficulty is only adjusted every 2016 blocks, what would happen if hash rate was to decrease rapidly? Wouldn't this cause blocks to be created less frequently and also making the time until difficulty is adjusted even longer?
Here's a scenario I had in mind, please point out any errors in it:

Some event causes people to lose faith in Bitcoin.
Those people sell off a lot of Bitcoins, causing the value of a Bitcoin (compared to e.g. a dollar) to drop a lot
Miners (who pay their electricity bill in dollars) find that mining is no longer profitable and a lot of them quit (until it is once again profitable)
The time between blocks has now increased (let's say to 15-20 minutes) since difficulty has not yet been adjusted.
People experience that the Bitcoin network is slow, it takes a lot of time to get transactions confirmed, and starts to lose faith in Bitcoin. Go to (1).

So, could this cause a downward spiral of the faith in Bitcoin?

A:

Yes, it could. It's not very likely, but it could happen.
However, one thing to keep in mind is that Bitcoin is incredibly resistant to these kinds of problems. Everyone who participates in the Bitcoin network has an incentive to keep that network useful. So a new client with a different difficulty algorithm could be released in a few days and the network transitioned in less than a week if needed. The difficulty adjustment could be changed if it needed to be.
For one thing, the "6 confirmations" rule is way overkill. People could compensate just by accepting 4 confirmations for transactions under $10,000 or the equivalent.
Ideally, people would see this risk coming several months away and could deploy a fix before it was needed. If circumstances in any way suggested that this was a realistic possibility, even in the absence of an actual attack a community consensus and transition plan could be developed and implemented. Alternative difficulty algorithms have already been proposed and even implemented (in other block chains) that don't have this issue.
Right now, I think such a change would be a bad idea. The problem is very unlikely, and any mass change in the logic of Bitcoin could undermine confidence in the long-term stability of the system. People might think "if they change the difficulty algorithm today, maybe they'll change the Bitcoin generation rate tomorrow".

A:

Yes. If the has rate decreases rapidly, the number of blocks produced per day will also decrease and, as a consequence, difficulty will take much longer to be updated. However, I think that your scenario is unlikely to happen. 
The mining network is relatively big at the moment so it will not disappear suddenly. Even if the price sinks, there are miners with cheap/free electricity that want to recover the money invested in mining rigs so they would be the last to leave. A predictable difficulty decrease is also a great opportunity to come in and collect easy profits when the 2016th block completes. 
If a big security flaw is found, a new client can be released and fix any of these issues. Bitcoin is very flexible, like David Schwartz said.

