We don't believe there's a place for women elders in the church. When the apostle Paul said that a woman should not "teach or exercise authority over a man" (1 Timothy 2:12), he did not follow that statement with a cultural argument. Rather he went all the way back to creation to show that women weren't intended to dominate men (vv. 13-14). The reasons he gave are that the woman was created after the man, and that she was deceived when acting independently of his leadership.
Paul goes on to say in 1 Timothy 2:15 that "women shall be preserved through the bearing of children if they continue in faith and love and sanctity with self-restraint." That verse is not talking about women's eternal destiny, but means that they are saved from being second-class citizens through the privilege of rearing children. God designed a woman to fulfill a role in the home that no man ever can (Proverbs 31:10-31; Titus 2:4-5).
Our society's current thinking on the woman's role is contrary to the priorities revealed in the Bible. Genesis 3 explains why that conflict exists. After the Fall, God told the woman, "Your desire shall be for your husband, and he shall rule over you" (Genesis 3:16). Genesis 4:7 helps us to understand what that verse means. There God told Cain, "Sin is crouching at the door; and its desire is for you, but you must master it." Exactly the same phrase is used in both passages. So in the same way sin tries to dominate us all, fallen women desire to overpower their husbands, and fallen men tend to oppress them in the same way sin oppresses the sinner. The intended balance, of course, is achieved when men and women lead and submit in a godly manner (Ephesians 5:22-33).
For further study:
John MacArthur, God's High Calling for Women (tape series), "The Subordination and Equality of Women" (tape 1844), "The Role of the Godly Woman" (tape 1845).