thanks for the question. its little unusual to have continuous eye discharge since birth. kindly start moxifloxacin eye drops 1 drop three times a day if you have been using gentamicin for longer duration. kindly clean the eye with sterile wet cotton from inner to outer side in one go. be gentle and avoid trauma. i do feel that you should look for swelling at the inner side of eye and excessive tears. if so it indicates poor drainage. in that case it might explain the recurrence of infection. also simple precautions like washing hands and cutting your and babies nails before handling baby would help.