What does Paul promise when prayers are voiced? He does not promise that external tribulations will immediately evaporate, nor does he assure instantaneous biochemical normalization. Instead, he writes that the peace of God, which surpasses all human understanding, will guard believers' hearts and minds in Christ Jesus.
The Greek word for "guard" is phrouresei, an explicitly military metaphor. Philippi was a Roman military colony, populated by retired legionaries accustomed to garrison guards patrolling city ramparts. Paul uses this vivid picture to reassure them: God's presence garrisons the vulnerable spirit against despair. This peace is not the absence of trouble. It is an anchoring presence holding steady while the storm rages.
Peace that surpasses understanding by definition makes no intellectual or environmental sense. It coexists with physical trembling, medical diagnoses, grief, and tears. Sanctification is not emotional anesthesia. Walking through suffering with integrity reflects true Christian spiritual maturity far better than pretending pain does not exist.