The present invention provides protease-resistant peptides, methods of making such peptides, as well as compositions comprising protease-resistant peptides and method of treatment utilizing such peptides. A combination of lipidation of certain amino acid residues and substitution of alpha-methyl functionalized amino acids for natural amino acids has been determined to produce protease-resistant peptides. Specifically, the peptides comprise the amino acid sequence H(Aib)EGS-(a-MeF)TSDV-(a-MeS)SX13LE-GEAA(a-MeK)-E(a-MeF)IAX25-VVEGG, wherein X13 is a lipid modified K, and X25 is a lipid modified K. These protease-resistant peptides are useful for treating or preventing a disease or condition in a subject caused or characterized by hypoglycemia or impaired insulin release.