Accepted answer
six weeks is 42 days, which at room temperature is on the order of 141 refrigerated days. Room temperature is not a number, so take the pharmacopoeial 20–25 °C and its 22.5 °C midpoint: 17.5 kelvin above the 5 °C middle of a 2–8 °C refrigerator. The ten-degree rule of thumb — degradation rate roughly doubling per 10 K — puts that at about 3.4 times the refrigerated rate. It is an order-of-magnitude statement about a rate, not a shelf life, and the top of the 20–25 °C band runs about 1.4 times faster than the bottom of it. In solution the routes that matter are hydrolysis of the backbone, deamidation at Asn, and physical association — the first two cost content, the third costs neither until it precipitates. Over 42 days at room temperature you should expect all three to have moved, and a purity figure to have noticed only some of them. Reconstituted material has no certificate; the one in the box describes the powder.
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.
Light exposure matters for tryptophan-containing sequences and for anything with a chromophore. Amber vials and a closed box are free mitigations.
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.