2 Timothy 4:20 Erastus remained at Corinth, and I left Trophimus, who was ill, at Miletus.
ooops...you’re right. Three, and counting...
First, it is wrong to think that someone can be healed solely on the faith of another. Jesus couldn't heal all those He wanted to heal in His hometown of Nazareth Mark 6:5-6 because of their unbelief Matt 13:58, not His.
Also, it sometimes takes time to receive a healing. This verse didn't say that Trophimus stayed sick. He may have but he may have just had a little difficulty receiving his healing and Paul didn't have time to wait on the manifestation. It's possible that Trophimus was healed and caught up with Paul or ministered in some other way.
It's also possible that Trophimus just quit believing God so Paul decided to leave him there sick. There are other possibilities, but there is no reason to interpret Paul leaving Trophimus sick at Miletum, as some indication that God doesn't want us to be healed. You can, though, if it makes you feel better.