I know too many wonderful saints of God who have spent good amounts of time on a sickbed, and it had nothing to do with sin in their lives. Secondly, what about sick children? Are they ill because of sin?
Everyone dies and everyone suffers from sickness at some point in their life. It's part of the bane of humanity. Thank Adam and Eve for messing things up for us!
The day your baby is sick will be the day you know it isn't because of sin. It's just because. Christianity doesn't protect us from hardship. It doesn't protect us from illness. It just allows us to lean on Someone when we are weak or troubled.
The scripture you provided doesn't say that a man's sins are forgiven and then he is healed. It says that the "Lord shall raise him up; AND if he have committed sins, they shall be forgiven...."
Where I will concede a small point is on the context of verse 16--I believe that the effectual fervent prayer of a
righteous man is worth a lot--and that of an unrighteous man may not carry as much weight--therefore when a righteous man asks for healing, perhaps God is more likely to give to him than the unrighteous man. But then, I know that it rains on the just and the unjust...right?
I do also believe that there are natural consequences of sinful or imprudent living that affect ones health--when we treat our bodies badly with substances or a poor lifestyle, then we may be sick later in life. My father was a heavy smoker and drinker (and occasional drug user) before he was saved at age 39, and he still suffered the effects of those things later in life, even though he served God.
If a woman chooses to prostitute herself, and catches a disease, and then is converted...will she necessarily be healed of her disease? Maybe, maybe not. Some consequences do not go away just because God saves our
soul.
But I'm not sure that God punishes sinners with illness. If that is the case, why aren't all the Christians thriving, and all the sinners dying young? Why are so many Christians sick and so many sinners healthy?