The part that matters: freeze-thaw damage happens at the moving ice front, not at the storage temperature. Once the sample is frozen solid and cold, very little is happening. The damage is done during freezing and thawing, which is why the number of cycles matters and the duration of the hold mostly does not.
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.
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.
Deamidation kinetics for asparagine in peptides are well characterised and strongly sequence-dependent: the residue following the asparagine dominates the rate, with glycine and serine at the n+1 position accelerating it by an order of magnitude relative to bulkier residues. That is why two peptides in the same buffer at the same temperature can have quite different shelf lives.
Store solid, store cold, store dry, and reconstitute what you will use rather than what fits in the vial.