Very interesting observation. I know that Smith Wigglesworth, a very powerful evangelist in the early 20th century, struggled with painful kidney stones, and in spite of healing countless people and raising many from the dead could not get healing for himself (you may not believe this, but his miracles are widely known, and numerous first-hand testimonies have been written about him and the way he lived his life).
My personal opinion on this is that the kidney stones were there because Wigglesworth by his own admission had a white-hot temper, and said he sometimes turned white as a sheet he was so angry. I think they may have been there as a mild form of judgment from God, that he not overdo it in his impatience with others. People with extraordinary faith and power tend to be impatient with others who do not live up to the same expectations as they have for themselves.
As for Timothy, a little stomach trouble doesn't sound all that bad, but things like chronic anxiety and fear can also cause health problems, and someone was showing me just the other day how it's pretty clear from scripture that Timothy walked in fear of what others might think of him, being much younger than many of the men he was given charge over in the Lord.
