I started trying to write you a bit about adhesives but, like everything else, a little background helps: in this case, about the word “archival.” Because all of these things come up in the adhesives discussion, let’s start here. Sorry if it’s boring… it’s good for you.
Acid content is generally what people think of in relation to whether something is archival, in particular “acid free.” Acids generally cause the degradation of cellulose (paper), which is why you don’t want anything acidic involved in bookbinding or other paperwork. But acid-free now doesn’t mean acid-free later: many materials, including cellulose, produce acid over time as they degrade (which then catalyze further acid production and further degradation. For this reason a lot of paper, for example, is manufactured with a “buffer” of something basic that can react with acid as it’s produced to neutralize it. Also, a slight amount of acidity is exponentially less damaging than a larger amount (review the pH scale if you want; I won’t force it on you here). If the pH of a paper measures 6.8, sure, it’s not neutral, but it’s not that bad. (Paper isn’t really the subject here, but it’s worth mentioning that lignins also catalyze degradation, which is why you might see paper labeled as acid- and lignin-free, and why you should be wary if you don’t.)
When we talk about archival materials in conservation, we look at other factors as well. Optical properties, for example; many materials yellow as they age, and ideally we want to change the object as little as possible, even if it’s only aesthetic. It’s not, of course, only an aesthetic concern: consider a tracing paper pasted to a fragile old printed rag paper as a repair, and the legibility of the text as the tracing paper turns yellow over time. (The reason it turns yellow has to do with its bonds rearranging in a way that makes the material absorb wavelengths of light in the blue spectrum–this you can read more about elsewhere if you’re interested.) From the point of view of the artist I think you can see without me pointing out the importance of understanding this.
Removability/reversibility/retreatability: hot topic in conservation, maybe less relevant to art but a worthwhile thought anyway. With the mindset that the future might decide our treatments problematic or more skilled approaches develop, we try to only use adhesives which could be removed later, or at the very least cause the least problem to future treatment. Old animal glue on reacts to water, so we can remove it. Old PVA from a repair … much less so.