Accepted answer
To be exact about it, 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.
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.
Mechanically, a domestic freezer holds roughly minus eighteen degrees and cycles by several degrees on its defrost schedule, which for a lyophilised solid is entirely adequate and for a frozen solution means repeated partial melting at the surface. If you are going to freeze a solution, an unopened chest freezer is materially better than the compartment in the top of a fridge.
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.