Accepted answer
At 4 °C the question is which route is fastest, not whether hydrolysis happens — and the routes do not share an activation energy, so their ranking changes with temperature. 4 °C is the condition the rule of thumb is anchored to, so it is the baseline rather than a multiplier: everything else in this thread is quoted relative to it. That multiplier is an average over every route at once, which is exactly why it cannot tell you which one wins. Backbone amide bonds cleave, so every product is shorter than the parent and the mass ladder they leave behind is the evidence that it happened. So the way to answer it for your vial is to pick the method that sees hydrolysis specifically and run it against a control held cold, rather than to infer a mechanism from a purity number that averages all of them.
Answer first: the degradation pathways worth knowing are hydrolysis, deamidation, oxidation, aggregation and adsorption, and each has a different trigger and a different mitigation.
Deamidation converts asparagine or glutamine to the corresponding acid via a succinimide intermediate, adding one dalton. It is base-catalysed, accelerates above neutral pH and is the dominant aqueous pathway for many peptides.
Stated carefully, hydrolysis cleaves the backbone, most readily at aspartate-proline and aspartate-glycine sequences, and is acid-catalysed. In a dry solid it barely proceeds at all.
Deamidation via the succinimide intermediate is well characterised, with sequence-dependent rates highest for asparagine-glycine motifs.
At dilute concentrations, suspect adsorption before you suspect chemistry.