What limits the half-life of your protein - if its proteolysis, a protease-deficient strain might help. In any case, let the cells grow to fairly high density before you induce, since you need to harvest relatively soon after induction. You may also try whether your peptide has a longer half-life if expressed as a fusion protein. Depending on how critical the most N-terminal residue is, you could, for example , release your peptide by TEV cleavage from an N-terminal fusion partner, this would only leave a Gly or Ser on the N-terminus of your peptide.

You don't say anything about the size of your peptide. If it isn't too long you can synthesize it rather than express it.

tanks all above,

I calculated half life of the peptide with protparam. Size of the peptide is about 6.8 Kda and synthesize of the peptide is very expensive and isn't purpose of our research.