What is the ruling on repeatedly exiting and re-entering prayer due to the obsessive thought of not contemplating the phrase "Allahu Akbar," or the occurrence of sexual images during the takbir, or an error in pronouncing the takbir, and can such behavior lead to the loss of faith?

What is happening to you is from the satanic whisperings, which have no cure other than ignoring them, disregarding them, and paying no attention to them. So, you must resist these whisperings with all your strength. Do not cut off your prayer once you have entered into it, no matter how much Satan deludes you that you have not pondered the Takbir or that you uttered the Takbir incorrectly. Do not pay attention to any of this, and continue with your prayer. Have a good opinion of Allah Almighty and strive in supplicating Him to strengthen you in faith, and seek His help in repelling this whisper.