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.
The 28-day figure for a reconstituted preserved vial is microbiological, not chemical. Chemically, a well-behaved peptide at 5 mg/mL at 4 °C will typically lose well under a per cent of content per month. The reason to respect the date is bioburden, and bioburden is a function of how many times you have opened it, not of the calendar.
On re-freezing something that thawed in transit: if it arrived as a lyophilised solid that warmed but never got wet, re-freezing costs you nothing except the thermal cycle. If it arrived as a solution that thawed, re-freezing adds a second transition and therefore a second dose of ice-front shear. The asymmetry is worth internalising.
General guidance on lyophilised peptide storage from the major synthesis houses converges on minus twenty degrees for long-term storage of solids and refrigerated storage for solutions in use, with the explicit note that repeated freeze-thaw of solutions should be avoided. It is consistent advice precisely because it follows from the chemistry rather than from a study.
I would be careful about generalising across sequences. Stability is sequence-specific, and a rule derived from semaglutide will not transfer cleanly to a tri-agonist with different residues in different local environments.
Store solid, store cold, store dry, and reconstitute what you will use rather than what fits in the vial.
edited 2 Mar 2025 by seamus_brady — corrected a unit error in the worked example