Terry Coxon has written an article called "How the Fed Could Become Insolvent". If you haven't seen it, it is certainly worth a read. He basically points out that if interest rates rise, there will be a certain point where the Federal Reserve is operating at a loss.
I don't think this means that the Fed becomes insolvent and he even acknowledges this. His conclusions are similar to mine in that the Fed will have more limited choices as rates rise. I think the Fed will eventually have to choose between hyperinflation and depression and I think and hope it will choose the latter.
I generally agree with what he says and I think interest rates will play a key role when we start to see things unravel. But in the grand scheme of things, a loss to the Fed is not that big. The bigger issue is the national debt, which is now over $14 trillion. The Congress will have to pay interest on this debt and when it has to rollover debt or issue new debt, it will be at higher rates when rates do in fact rise. The Congress will either have to spend less, tax more, or get the Fed to create more money out of thin air. The first two options are limited. Congress could certainly spend a whole lot less, but even if it cut the budget by one-third, there would still be a yearly deficit right now. The problem is that the politicians are unwilling, at least at this time, to make any substantial cuts to the military or "entitlement" programs.
Raising taxes won't really help either. It will just stifle the economy that much more and it may even lead to less taxes collected by the government (we'll give Art Laffer, a non-Austrian economist, a little bit of credit here).
So basically, that leaves the Fed to create more money. More inflation will lead to even higher interest rates down the road, just as Coxon has written in his article.
The Fed will eventually have to slam on the brakes to avoid hyperinflation and I think it will. The ultimate solution will be for government to be dramatically cut, including the military, Social Security, Medicare, and pensions. The other thing that will probably happen is a default. It will happen first through inflation and then there will be some kind of outright default. You don't want to own a lot of government bonds when that happens.