Can a Muslim enter Paradise if he repents his past (bad) actions when he is about to die?

The following verse of the Qur’ān spells out the conditions of repentance:

Allah accepts the repentance of those who do evil while being overcome with emotions and repent soon afterwards; to them will Allah turn in mercy. For Allah is full of knowledge and wisdom. Of no effect is the repentance of those who continue to do evil until death faces them and he says: Now I have repented indeed; nor [the repentance] of those who die rejecting faith1 [avail them]. For them have We prepared a punishment most grievous. (4:17-18)

If we deliberate a little on the above quoted verses, it becomes clear that the Almighty will necessarily accept the repentance of people who repent immediately after doing a sin not in cold blood but in a state of emotional frenzy, on the contrary, people who postpone their repentance till death approaches them will never be forgiven by the Almighty. Similarly, the repentance of those who die in a state of rejection of faith* will not be accepted. However, these verses do not mention the case of people who do not repent immediately afterwards nor do they defer their matter of repentance to their death. This lack of mention produces both fear and hope at the same time in such a person. What will happen to him will only be known on the Day of Judgement. He should try to seek forgiveness from the Almighty as much as he can.

1. The actual word used is Kuffār (Those who have rejected faith). These Kuffār must not be confused with the non-Muslims of today. People become Kuffār after they deliberately reject the truth unveiled to them. Only the Prophet (sws) and his companions were in a position to unveil the truth in its ultimate form. Today, no Muslim preacher can be in this position as is specified by the Qur’ān in 2:143. Consequently, no non-Muslim can be called a Kāfir in these times. Only on the Day of Judgement will we be able to know whether a particular person of our times a Kāfir or not.