How can a protein folding transition state have zero lifetime?
I don’t know where the person from the Google Groups you quote got the information that a transition state is "presumed to have zero lifetime", but a far as I can tell it is wrong. On the contrary, the existence of transition states is postulated in transition state theory (TST), which evidently implies that within the TST framework transition states have non-zero lifetime. Existence clearly contradicts zero lifetime: if some object has zero lifetime, what do you mean then by its existence?

Next, while the lifetime of a transition state in TST is postulated to be not zero, it is also proposed to be quite small, on the order of the time of a single molecular vibration ($10^{-13}$ seconds). Why do we have to make such a proposition? Well, transition state can be defined as the state corresponding to the highest potential energy between the reactants and the products (i.e. along a reaction coordinate) such that the probabilities of forming the reactants or products are equal. On potential energy surface (PES) then transition states correspond to the so-called saddle points (first-order saddle points, to be more precise), which, loosely speaking, can be thought of as a maximum in one direction (along the reaction coordinate) and minimum in all other directions. And structures that correspond to maxima (even in one direction) on PES) are unstable: once a system is at a maximum on PES it will almost instantly fall from it to one of the two neighbouring minima (either to reactants or to the products side).

Due to small assumed lifetime of a transition state, it is often said that "no physical or spectroscopic method is available to directly observe the structure of the transition state" (quote from Wikipedia article on TST). Although, with femtosecond IR spectroscopy one can actually observe molecular structures extremely close to the transition state structures. The practical problem is that quite often along the reaction coordinate in addition to a maximum corresponding to transition state between the reactants and the products there exist a minimum (or few) corresponding to the so-called reactive intermediates, and it is quite difficult to distinguish between transition states and reactive intermediates. 

Note here that reactive intermediates correspond to minimum in all directions on PES, and are thus stable, or, to be more precise, metastable, since they are high-energy molecules which are quickly converted into more stable molecules (either another reactive intermediate or eventually the products). Reactive intermediates are also short-lived but with lifetimes appreciably longer than a molecular vibration, so they cannot usually be isolated, but they can be observed with the already mentioned femtosecond IR spectroscopy.

To summarise:


One should not in the first place think about transition states being real (and consequently detectable). A transition state is a part of a model description of a chemical reaction introduced by TST, where we just postulate their existence, and say no word on are they really exist or not. Irregardles of their real existence, transition states exist in our model description, and their existence implies non-zero lifetime.
Besides, with femtosecond IR spectroscopy it is possible to directly observe a transition states for some chemical reactions and it was actually done.