No that's not true. The claim that if it becomes unprofitable mining will decrease, miners will stop, and it will become profitable again. That's ok. It doesn't matter.
The security of the network is determined by hash. A decrease in mining is a decrease in hash which is a decrease in security. If hash declines the value of bitcoins will decline. The hash determined the value of the bitcoin, nothing else. The hash gives the bitcoin security.
Once hash decreases vale decreases. The hash has to keep growing for value to icrease.
Your assumption that bitcoin derives it's value solely from security is false. A large part is the security, yes, but it also derives from:
Convenience. It's DAMN easy to send someone a bitcoin.
Intrigue. The concept is really clever.
Freedom to property.
Cost. It's a LOT cheaper to send someone internationally 1btc than it is 20 dollars.
If the hash rate decreases (or stagnates), that does not guarantee that someone will be able to overwhelm the network instantaneously. They still have to ACQUIRE a substantial majority of the networking power. At the CURRENT volume of miners, that's more than the top 500 supercomputers combined. In a stable, vast reaching economy, "competition" (I use the word here for lack of a better term, not to imply that block solutions is a race) for the block solutions would be extremely high, and thus there would be several hundred times more computing power devoted to bitcoin.
Transaction fees will more than cover the costs of incentivizing miners, as I outlined above. What you seem to think is that the value of bitcoins at this point will be extremely fluid: A TINY decrease in security will cause mass panic and devalue the currency, causing a cascade. Bitcoins will become stickier than that. In the same way that you cannot notice a 100w lightbulb among 100 other 100w lightbulb, there's a certain point at which the fluctuation of security in the system is undetectable. The value of bitcoins will stabilize. The value of a dollar is not subject to stock-like panic swings, and in the presence of a rich economy, neither will bitcoins.
Similarly, the security of the system as a whole is subject to the same sensory threshold phenomenon. The difference in security between 100THash/s and 99THash/s is not equivalent to the difference in security from 2THash/s to 1THash/s. Just because it drops by 1 THash/s in the future doesn't mean it will have the same risks assosciated with dropping by 1THash/s today.
Finally, someone with substantial control of the computational power of the network has only limited attack vectors on the system. He can claim he did not spend money which he did for limited amounts of time. The longer in the past he wants to rewrite this "history", the harder it takes, and he can never say that you gave him coins that you did not. The likely payoff for this in regards to the amount of computing power it would take to compromise a vast system that satoshi envisioned as a stable, worldwide economy would arguably not be worth it. Seemingly against intuition, and in one of the most beautiful aspects of the bitcoin system, when dealing with the types of resources required to complete these attacks, it's likely more profitable to be honest than it is to be malicious.
No, the difficulty would also adjust down. It's adjusted such that a block is generated roughly every