The Prophet (peace be upon  him) said: "Between a man and polytheism (shirk) and unbelief (kufr) is the non-performance of the prayer." [Sahih Muslim]

This Hadith indicates the importance of the five daily obligatory prayers. It describes the performance of the prayer as the line of demarcation between a believer and an unbeliever.

While the importance of the obligatory prayers cannot be stressed enough, and not performing them is a major sin, nevertheless, missing the prayers does not take one out of Islam.

The Prophet (peace be upon him) said: "Allah has made five prayers obligatory: whoever performs their ablution well and prays them in their time, completing the bowing, the humility, and the awe that is due in them, has entered a solemn pact with Allah to forgive him. And whoever does not, has no pact with Allah: should He want, He will forgive him, and should He want, He will torment him." [Abu Dawud]

The evidence from this Hadith is that the case of someone who does not pray is up to Allah's considered choice, meaning that Allah could choose not to torment him, while it is necessarily established that unbelievers will be tormented and enter Hell. This indicates that someone who neglects to pray is not an unbeliever. However, he could still enter Jahannum as punishment for his sins and after his purification he may then enter Jannat.

To conclude, praying is highly rewarded by Allah, as Allah's forgiveness which one receives as a result of praying, entails the entering of Jannat, and this is priceless. Not praying is a major sin, which brings one close to disbelief. Nevertheless, so long as someone accepts that it is an obligation to pray, not praying does not necessarily take them out of the fold of Islam.