Abraham shows persistence in the way he pleads with God to have mercy on the righteous and not to slay them with the wicket. He starts by asking God if He would destroy even if there are fifty righteous people in the city and right down to ten. abraham needed to know if God would save even if there are ten righteous in the city.
He did not just ask once or twice he really wanted God to save any one who was righteous and he knew well that God was a just and merciful God who would not bring evil to any one of HIs children. I suppose Abraham just needed to know if God would show mercy and saved those who put their trust in Him.
Persistence is necessary in prayer as it create a faith building mechanism within each christian. Some times we give up so easily because we don't see answers to prayers. So being persistent encourages us to stand in faith believing God for answers. God wants us to be like Abraham, just go before Him and continuing to seek Him until we hear from him.
I don't think God wants to see His children give up easily. Jesus gave a parable about a woman who bothered a judge by persistently going to sort some issues out until he gave in to her. She was so persistent that she wouldn't leave him alone until he gave her the answer she wanted. God I believe wants His children to do the same when they go before Him in prayers.
Praying through for me often comes when there are difficult issues or intercessory prayer for others or situations I become aware of.
One of my most difficult times was when my dad passed away a few years ago. My relationship with mom was not the best and for me a best friend and mentor was gone forever from this world. I went through a period where it felt lonely and no one cares. So God came to the rescue and in the midst of my darkest moments, He told me to forgive and love mom regardless. All I needed to do was to pray for her and trust Him to restore back what the enemy robbed me of for so many years. So for months I spent time praying that God would heal mom and deliver her from bitterness, restoring a relationship etc. No visual change as a matter of fact, it seemed things got worse as i continue to pray. Bit by bit God removed things in my own life that caused me to see things in the way I wanted, and allowed me to see mom in His eyes and His grace. After 3years of praying I can surely say, that God is gracious and merciful. He restored my ralationship with mom and it's a beautiful friendship now blooming. It didn't take a week or months, it took years of sowing, pruning and watering in the prayers!