Non-ribosomal peptide synthesis: why Glutathione cannot be produced by the ribosome?
It's definitely not the length. Although ribosomes can't make really really small peptides because they need something to hold onto and in any case proteins start with methionine(usually), there are workarounds. There's no reason why a tripeptide couldn't be coded for by a gene directly.

The 'traditional' method of producing very short peptides is producing a longer protein and cleaving off a chunk of it, which works great for signal peptides and a number of other systems. Very small peptides are more efficiently made by enzymes like this but in principle there's no reason to besides efficiency and complexity. (You need a special protease for each small peptide etc etc etc)

However, this gamma bond is a different beast entirely, and no ribosome could ever produce it, even in the middle of a longer protein. Amino acids 'snap' together in a very specific way. The amino group bonds to the carboxyl group of the previous amino acid, making a chain. The side groups of an amino acid aren't involved. Like Legos that snap together only one way and can be any color or have any designs on the side. The difference here is glutamate has a carboxyl group as part of its side chain. It's like a Lego with holes on two sides. The NRPS here connects the cysteine to the side chain of the glutamate instead of the 'bottom' where it would go if a ribosome-synthesized glutamate-cysteine bond. 

This gamma bond also explains the increased longevity of the product. Proteases aren't designed for things that look like this. The gamma bond doesn't 'fit right' in the protease active sites and therefore activity is slower.