Accepted answer
The relevant detail is that the lyophilised solid is far more robust than anything anyone says about it, and the solution is far less robust. Most of the confusion in this area comes from advice about one being applied to the other.
Adsorption to the container is a real loss at low concentration. For a peptide at 0.1 mg/mL in an untreated glass vial, single-digit percentage losses to the wall are plausible; at 5 mg/mL it is negligible. This is one of several reasons not to reconstitute to a very dilute working solution and store it.
Practical thermal arithmetic for a shipment: a single 250 g phase-change pack in a thin-walled polystyrene box holds sub-ten-degrees for roughly 24 to 48 hours in a 25 °C ambient, and considerably less at 35 °C. Any lane taking eight to fourteen days is therefore not temperature-controlled for most of its duration regardless of what was in the box, which is the argument for shipping the material lyophilised.
The licensed semaglutide and tirzepatide presentations carry in-use periods of several weeks at room temperature in their labelling, which is the closest thing to real stability data in this space — and it applies to a buffered, surfactant-containing, preservative-containing formulation, not to a reconstituted research vial.
The limitation is that you cannot detect slow aggregation by eye until it is well advanced, so a clear vial is weak evidence of an intact one.
The single highest-value change most people can make is buying a cheap logging thermometer, because it converts an assumption about their storage into a record.