What does Acts 20:26 mean?

Paul is in Miletus, speaking with the elders of the church of Ephesus. He has just told them he will soon be imprisoned in Jerusalem and never see them again (Acts 20:22–25).

His words here are those of a prophet. When God called Ezekiel to be His prophet for the Jews in exile in Babylon, He set very strict ground rules. God told Ezekiel that if He gave him a warning and people died because Ezekiel refused to pass on the warning, Ezekiel was accountable for their deaths. If Ezekiel did pass on the warning but people died because they ignored it, their deaths were on their own heads (Ezekiel 3:17–21). As a living representation of the importance of Ezekiel's commission, God made him mute, except for God's messages, until the exiles received word that Jerusalem had fallen (Ezekiel 3:26–27; 33:22).

There's no indication that God gave Paul a similar warning, but Paul certainly lives as if He had. As he says to the church in Corinth, "For if I preach the gospel, that gives me no ground for boasting. For necessity is laid upon me. Woe to me if I do not preach the gospel!" (1 Corinthians 9:16). He will later write Timothy, "Preach the word; be ready in season and out of season; reprove, rebuke, and exhort, with complete patience and teaching" (2 Timothy 4:2). Paul speaks to government officials, Jews, Gentiles, women, Greek philosophers, and kings (Acts 13:7, 16, 46; 16:14; 17:22; 18:7; 25:23). He preaches at synagogues, riversides, prisons, homes, marketplaces, and the Areopagus of Athens (Acts 14:1; 16:13, 25; 17:17, 22; 18:7; 26:1). He even tries to preach to the mobs that wanted him dead (Acts 19:30–31; 22:1–22).

If anyone around Paul does not accept Jesus as their Savior, it isn't because Paul failed in his efforts to convert them.