Lyophilized peptides are made to remain stable in room temperatures for up to 4 weeks or more in an un-reconstituted state. The official recommendation is to store all lyophilized peptides in - 20C (in a fridge or freezer) until you are ready to start your research. If kept in a freezer prior to reconstitution, peptides have a shelf life of 6-9 months, depending on the peptide.
Once a peptide has been reconstituted it must be refrigerated and will be good for 2-4 weeks depending upon handling.