Trophimus at Miletus

In my post, Cessationists, Healing, and Acts, I said the following:

"II Timothy 4:20 says that Paul left Trophimus at Miletus sick, which means that he didn't heal him. When was Paul at Miletus? In Acts 20:15-17. Yet, Paul had the gift of healing after he left Miletus. In Acts 28, he heals the inhabitants of Malta."

It turns out that I wasn't entirely accurate, for Acts 20 does not present the time when Paul left Trophimus in Miletus. Rather, Trophimus left Miletus with Paul to go to Jerusalem (Acts 21:29). That's one reason Paul got in trouble: Paul's Jewish opponents thought he brought the Gentile Trophimus into the temple.

So when did Paul leave the ill Trophimus in Miletus? Some say it was when he was on his way to Rome for trial. If that is the case, then my argument has merit, for Paul would come to Miletus (in Asia Minor) before arriving at Malta, where he did his miracles.

But others think that Miletus in II Timothy 4:20 is actually Malta, which in the Greek is "Melite." If that's the case, then the cessationists may have the upper hand. They could argue that Paul did his healing miracles in Malta, after which his powers ceased. When he was leaving Malta, he left Trophimus sick. Trophimus apparently got sick a little too late! He should've done so before Paul's healing ability went away.

Acts 27:5-7 presents Paul's ship going around Asia Minor, but it doesn't say it stopped at Miletus. And Acts is usually pretty specific about where Paul stops on his journeys (see Acts 21:1-3).

So I'm not sure when Paul left Trophimus in Miletus sick.