Peptides are more robust than their reputation suggests in the dry state, and more fragile than expected once in solution. Understanding which stresses matter, and when, saves a lot of unnecessary worry about shipping and a lot of avoidable loss in storage.
In lyophilized form, moisture is the primary enemy. Water enables hydrolysis of the peptide backbone and gives residual enzymes something to work with. This is why vials are sealed under vacuum or inert gas, and why letting a cold vial warm before opening matters more than most handling steps. A few days at ambient temperature in transit is generally well tolerated by a dry, sealed vial; days of humidity exposure after opening is not.
Once reconstituted, the ranking changes. Temperature dominates: degradation rates roughly double for every 10 °C increase, so refrigeration is doing real work. Sequences containing methionine, cysteine, or tryptophan are additionally vulnerable to oxidation, and light accelerates it — an amber vial or a foil wrap is not decoration. Repeated freeze-thaw cycles are their own category of damage, which is the argument for aliquoting rather than thawing a single stock repeatedly.