How can a person still be Muslim if he reaches the point of being executed and still insists on not praying?

This is a very good question, but those who say that such a person is not a kaafir do not have a good answer. Shaykh al-Islam ibn Taymiyah (may Allaah have mercy on him) noted that this confusion arose among the later fuqahaa, because this was not known among the Sahaabah, may Allaah have mercy on them. As the questioner says, it is not possible that a person who is threatened with execution for not praying would choose death over prayer if there was even an atoms weight of Islam in his heart. This confusion does not arise if we say that the one who does not pray is a kaafir. If we read what Shaykh al-Islam Ibn Taymiyah said about this matter, this will dispel any confusion.

He (may Allaah have mercy on him) said:

In the case of one who believes that prayer is obligatory yet still persists in not praying, the fuqahaa who have studied the matter in detail mentioned a number of points:

The first of them is this point, which was stated by the majority of them, Maalik, Al-Shaafai and Ahmad: if a person persists until he is killed, is he killed as a kaafir and an apostate, or as a sinful Muslim like other sinful Muslims, as stated in the two well-known views reported from Ahmad? Such detailed discussion was not reported from the Sahaabah, and is excessive and futile.

If the person believes in his heart that prayer is obligatory, this will not allow him to persist in not doing it until he is executed. Such a thing is not known among the sons of Adam, and has never happened in Islam. It is unheard of for a person to believe that it is obligatory and to be told, If you do not pray we will execute you and then to persist in not doing it even though he believes it is obligatory. This has never happened in Islam.

When a person refrains from praying until he is executed, he does not really believe in his heart that it is obligatory and was not doing it, so he is a kaafir, according to the consensus of the Muslims, as it was stated in many reports that the Sahaabah would consider such a person to be a kaafir. This is also indicated by the saheeh texts, such as the ahadeeth of the Prophet (peace and blessings of Allaah be upon him):

Nothing stands between a person and Kufr except his giving up prayer (narrated by Muslim).

The covenant that separates us from them is prayer, and whoever gives up prayer has become a kaafir.

Abd-Allaah ibn Shaqeeq said: The companions of Muhammad did not think that giving up any deed would make a person a kaafir apart from giving up prayer.

Whoever persists in not praying and never prostrated to Allaah at all until he dies, can never be a Muslim who believes that prayer is obligatory. Believing that it is obligatory and that the person who does not do it deserves to be executed is sufficient motive to make a person do it, for if a person has the motive and ability to do something, it should be done. If he is able to do it but he never does it, this indicates that the motive is not present in his case.

(Majmoo al-Fataawa, 22/47-49)

Please also refer to Question #2182

And Allaah knows best.