The King James Version uses the word "patience," which is not a wrong translation. However, for better understanding, more specific words should be used. Today, we generally think of "patience" as passive, whereas "persevere" or "endure" is more dynamic. The Greek word used in Hebrews 10:36 is hupomone. In his Complete Word Study Dictionary: New Testament, Spiros Zodhiates comments that it means "constancy under suffering in faith and duty." "Constancy" indicates that persistent effort is being made, in this case against a pressing trouble. He perhaps describes it even better by defining it as a "quality of character that does not allow one to surrender."
"Perseverance," "endurance," "constancy," and "steadfastness" all have a sense of activity, of actively straining against some pressure. Thus, as Hebrews 11 begins, the author approaches two related subjects: one directly, faith or strong conviction; and the other, perseverance, less directly. Hupomone, however, does not appear again until Hebrews 12:1.
The Hebrews badly needed both conviction and perseverance to meet and overcome their problems. These virtues go hand in hand, and they really cannot be separated because we operate on a different concept of time than does God. Compared to God, we operate on fast time. Almost everything in our lives seems to have to be done or received right now, or faith begins to evaporate and we lose heart. True faith, though, operates in a rhythm closer to what God does because, due to conviction, it is more in tune with Him.
Therefore, a convicted person not only believes that what God says is true, but he also trusts and willingly endures trials in an attitude of realistic hopefulness. He does not restlessly complain to God to fix things right away on his schedule. A person develops conviction by thoughtfully processing a great deal of God's truth and yielding to the evidence He provides.