A less-than-quick Google search links to an article on the doiSerbia website that seems to say that adjectives and nouns are probably most susceptible to diachronic change, but the conclusions were based on corpus analyses within the last half a century. I don't know how true this is but to each his own: there might be some truth in that, might as well not.
There's a generally-known and otherwise pretty unsourceable statement that most commonly used lexical items are the most prone to irregularity and change, which makes sense as they are more frequently used. Don't know where I heard it or picked it up, but I'm a firm believer in it.
This can be backed up by looking at the statistical fact that the copula, some elementary terms regarding kinship, obligation, quality and quantity (good, bad, big, small), grammatical polarity (yes, no), pronouns and numerals are most commonly irregular and exhibit unpredictable and unexpected changes and are the ones that most frequently show suppletive paradigms.
Even in highly regular languages that have a very high level of regularity, the copula and core terms have patterns that deviate from the norm (olla (to be), veli (brother) in Finnish, olmak (to be) in Turkish etc.) even while most of the rest of their vocabulary sticks to established and regular patterns.