Accepted answer
At minus 80 °C it can show up as either, and which one depends entirely on whether the product still elutes under the main peak. Purity is a ratio of areas, so a degradant only costs purity if the method resolves it. Content is a mass against a standard, so a degradant costs content whenever the parent is consumed — resolved or not. A stereocentre inverts. Identical mass, identical formula; only a chiral method or a peptide map with a chiral digestion sees it at all. That is why the two measurements are not interchangeable and why an unchanged purity figure after an excursion to minus 80 °C is weak evidence: the method may simply be integrating the degradant along with the parent and reporting the sum as one peak.
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.
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.
Cold, dry, dark, still. Those four words cover most of the mitigation.