Paul writes, "Trophimus I have left in Miletus sick." Evidently Trophimus had planned to come with Paul, but his illness changed their plans.
James writes, "Is anyone among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord. And the prayer of faith will save the sick, and The Lord will raise him up" (James 5:14-16). So why did't Paul pray for the man and The Lord heal him?
Scripture does not tell us if Paul had prayed or not (I an confident he did) nor why his friend was not healed. Paul earlier wrote to the believers at Galatia, "You know that because of physical infirmity I preached the gospel to you at the first. And my trial which was in my flesh you did not dispose or reject, but you received me as an angel of God..." (Galatians 4:13-14).
We do not know why The Lord had not yet healed Paul's friend. Nor do we know how Paul's physical infirmity provided the opportunity for Paul to preach the gospel to the Galatians. However, we can fairly conclude, God may have a purpose even in our illness.
