Should fractional reserve banking be prohibited through the bitcoin protocol or otherwise, and how could such a change be implemented? There's a massive macroeconomic debate between Keynesians, who want central banks to control the money supply, and Austrians who want no central banks doing any such thing--or at least competing currencies which provide an alternative to central banks which do.  Bitcoin, with its set mining schedule, takes a clear stand against the former and opts for what will in 2033 become a stable/deflationary currency. 

A debate which has not been settled, even among hardcore Austrians, is whether fractional reserve banking is good or bad for economies.  Similar to central banks, fractional reserve banking expands the money supply, but not at the fundamental level.  The effect is often the same, however, and the result is booms and inevitable busts as growing loans and investment cycle with contractions and bank runs.

For bitcoin enthusiasts who are skeptical about inflation, fractional reserve banking poses a similar threat.  As long as anyone except you are holding your bitcoins, there's no way to prove that your coins aren't being lent out at any possible reserve ratio.  Gresham's law suggests that 'bad money drives out good', meaning people will first use unsecure, inflationary currencies and hoard better ones.  Since bitcoin aims to be an optimal currency, it should explore avoiding the fate where it is bested by a regime which prevents fractional reserve banking.  

My question is:  Can fractional reserve banking be prohibited, technically, a) through a change the bitcoin client itself; b) in a customer-bank protocol; or c) in another cryptocurrency scheme. 

I don't know enough about public key cryptography, but I have an inkling that it would involve limiting return addresses, so for example, I send 10 bitcoins to address A, but those bitcoins can ONLY be sent back to an address I provide, and nowhere else.  Could that kind of scheme be implemented at any level, even just as an option?
No, you can't prevent fractional reserve banking technically. For example, IOUs can circulate just like Bitcoins and there's no technical means to stop it. Essentially, anything worth X Bitcoins (once risk and the like are factored in) can act just like X Bitcoins, even if it's not X Bitcoins. And since it's not Bitcoins, nothing Bitcoins can do can stop it.

Unless you foresee some massively powerful central coercive authority that prohibits it, you will always have fractional reserve banking. It just makes too much sense. It will happen absent the use of massive amounts of force.

There are trivial technical fixes to the "run on the banks" problem. However, there is still the very real "the bank is a crook" problem and the "the bank goes broke due to fundamentally unsound loans" problem.