Why did Abraham lie to Pharaoh about Sarah being his sister in Gen 12? It says that Abraham feared for his life (Gen 12:12). Does this mean Abraham didn't trust God in spite of the NT view that Abraham was a man of faith (Heb 11:8-12, Gal 3:9)? 

Why is the repeated mistake with Abimilech then recorded in Gen 20?
Regardless of his faith, Abraham was still a man - he had not yet been perfected: he was still on his walk of progressive sanctification. 

The same question could be asked as to why David sinned with Bathsheba, or why Samson fell for Delilah.

And any of countless more examples - the men and women portrayed in the Bible were not perfect (excepting Christ). Even Peter, who had been with Jesus since the earliest days of His ministry, denied him three times during the trial before the Sanhedrin.

Every instance is an opportunity to showcase God's faithfulness, mercy, and grace - even when his chosen ones fail Him.

Even those with the stoutest faith in God can forget or become fearful: while backsliding or temporarily turning from God to our own wisdom is never promoted, it is the entire life story that must be examined. When doing that with Abraham, it is obvious that though he was not perfect, he was following God.