It depends upon the brand of hgh. As others haved mentioned mixing it with bac water and storing it in the fridge will only extend that period. Some hgh can go bad really fast even before mixed at room temperature. When mixed and stored in the fridge most will last a fairly long time (months).
As far as I know, Jintropin and Saizen can survive normal room temperature during storage and shipping. However, only before the mixture or the reconstitution. All hgh brands need to be refridgerated after being reconstituted.