Degradation is not one process, and which one dominates depends on the condition you are asking about. In solution at refrigerated temperature the rate-limiting pathway is usually deamidation and hydrolysis; at room temperature aggregation overtakes them; frozen, the damage happens during the transitions rather than during the hold.
Freeze-concentration is the mechanism people miss. As ice forms, everything that is not water is excluded into a shrinking unfrozen fraction, so the local concentration of peptide, buffer salts and preservative rises sharply. If the buffer components crystallise at different rates, local pH can shift by more than a unit. That is why a phosphate-buffered solution can behave badly on freezing while an unbuffered one is fine.
Put another way, the temperature dependence is roughly Arrhenius over the range that matters, which in practice means every ten degrees of increase roughly doubles to triples the rate. Ten days at thirty degrees is therefore comparable to something on the order of a month or two at four degrees — bad, but not the catastrophe it feels like when you open a warm parcel.
Deamidation kinetics for asparagine in peptides are well characterised and strongly sequence-dependent: the residue following the asparagine dominates the rate, with glycine and serine at the n+1 position accelerating it by an order of magnitude relative to bulkier residues. That is why two peptides in the same buffer at the same temperature can have quite different shelf lives.
One qualification: none of this addresses sterility. A vial can be chemically pristine and microbiologically compromised, and a chromatogram will not tell you which.
Store solid, store cold, store dry, and reconstitute what you will use rather than what fits in the vial.