At minus 20 °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. Ordered beta-sheet assembly, effectively irreversible, and its endpoint is opalescence you can see rather than a peak you can integrate. That is why the two measurements are not interchangeable and why an unchanged purity figure after an excursion to minus 20 °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.
The relevant detail is that freeze-thaw cycling drives aggregation through concentration at the ice interface and pH shifts as buffer components crystallise out at different rates. Each cycle costs something.
Aggregation at air-liquid interfaces is established from surface-tension and particle-count studies and is the basis for anti-agitation handling guidance.
At dilute concentrations, suspect adsorption before you suspect chemistry.