All peptides are stored in lyophilized form at temperatures of -20 degrees Celcius some at -40 degrees Celcius or more.
This holds true for all peptides whether they are shorter chains made via the process of solid state synthesis or longer chains made via e. coli.
Here is an example for you. It is Fibroblast Growth Factor (bFGF) purchased by my lab from a leading facility. bFGF is 151 amino acids long.
"...bFGF is stable lyophilized for 6 months at -20 degrees C to -80 degrees C. After a quick spin [in the centrifuge], reconstitute in 500ul of 10nM Tris, pH 7.6 to yield stock solution of 0.1 mg/ml of bFGF. Reconstituted bFGF should be stored in working aliquots at -20 degrees Celcius for up to six months. Multiple freeze/thaw cycles will result in significant loss of activity.."
For longer term storage you did what you were suppose to do with your unreconstructed GH.
It is debatable (and may depend on the solution buffer) whether you can/should freeze reconstituted peptides. As you can see, instructions from the leading American manufacturer of peptides for lab use in the United States says you can for up to 6 months.
In some of my research I have discovered that if you have the coldest of lab freezers (-80 C) you can store peptides for 5 years w/ no significant loss of bioactivity.
One suggestion for you and all who read and store peptides in the freezer is to get some silica gel moisture absorbing bags to put in w/ your vials. Vaccum seal or at least squeeze out the air in the bag/container that holds the vials to be frozen.
Stop fretting.