It is stated in many prophetic traditions about the Last Days: concerning the tribulation and extreme trial that a believer at morning may turn to be a disbeliever by night, and the disbeliever by night may turn to be a believer by day ... or so.
Being a Muslim traditionally (in spite of the enthusiasm about the imams and sheikhs) will not save man, but the true belief and submission to God alone without associate or son in addition to working the righteous work may save man.