Colin, cyanotype is one of the most stable processes around, as long as you protect the paper from alkali conditions and you process them well. (If iron remains in the paper it would be detrimental in the long term; but this is a common handicap of all iron processes...) The very first cyanotypes made by Herschel himself (and Anna Atkins a little later - we are talking about 170 years here!) are still in good shape. It is true that the prints may show a little fading (reversible to some extent) when subjected to very strong / energetic light, but this is not an issue with normal indoor lighting conditions, especially so with UV protective glazing.
In short; don't worry about the longevity of cyanotypes, they're practically as stable as pt/pd prints and particularly much much more stable than untoned salt prints!