Unreconstituted (lyophilized) peptides can be frozen without concern—they're already in a very stable form. Reconstituted peptides should not be repeatedly frozen and thawed. Each freeze-thaw cycle can cause some degradation and aggregation. If you need to store reconstituted peptides long-term, keep them refrigerated (2-8°C) rather than freezing. If you have excess reconstituted peptide you won't use within a few weeks, it's better to reconstitute fewer vials at a time.