All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
The prayer is of great status in Islam; it is the second pillar after the two testimonies of faith. It is the first thing that a Muslim will be questioned about on the Day of Judgment; if he preserves it, he will be safe and successful, and if he abandons it, he will lose and fail.
Indeed, there is a severe threat for the one who neglects the prayer or abandons it. Allaah says (what means): {But there came after them successors who neglected prayer and pursued desires; so they are going to meet evil.} [Quran 19:59] Allaah also says (what means): {So woe to those who pray. [But] who are heedless of their prayer.} [Quran 107:4-5]
Therefore, you must observe the prayer on time while fulfilling its pillars and conditions.
It is known that the Thuhr prayer consists of four rak’ahs – for other than the traveler who shortens his prayers. So whoever leaves out two rak'ahs deliberately has indeed committed a heinous sin, and his prayer is invalid without any doubt. Whoever misses one of the pillars of prayer, such as rukoo’ (bowing) or sujood (prostrating) intentionally, then his prayer is invalid, let alone if he misses two whole rak'ahs.
Being tired does not justify shortening the prayer. You may delay the prayer until you feel better but perform it before the end of its time. In the fataawa of Noor ‘ala Ad-Darb, Shaykh Ibn Baaz was asked, “Is it permissible to delay the prayer when feeling very tired in order to rest for a while until I can perform it in a perfect manner? Also, is it permissible to repeat the prayer if one had performed it while one was distracted and was not concentrating?” He answered:
“The believing man and the believing woman must give due care to prayer and perfect its rukoo’ and sujood. However, if at the beginning time of the prayer he was tired, then it is acceptable for him to rest. It is better for him to rest provided that he prays it before its time expires, because if one performs the prayer, even towards the end of its time, while he is relaxed and prays it with humbleness and submissiveness, then this is better than praying it without humbleness and submissiveness, but in no case is he permitted to delay it until its prescribed fixed time expires. The prayer must be offered during the time of the prayer, and delaying the prayer to the middle of its time, or towards the end of its time for a valid need, such as tiredness or illness and the like, is permissible.”
It should be mentioned that fatigue that causes hardship to the person in performing the prayer on time makes it permissible for him to join between two prayers according to the view of some scholars, who consider that it is permissible to combine the prayers for a resident (i.e. not traveling) person when he faces hardship in case he does not combine them. Please, refer to fatwa 82828.
Shaykh Al-Islam Ibn Taymiyyah said, “Combining two prayers is for removing hardship; so if one finds hardship when performing each prayer at its time, it becomes permissible for him to combine between them; because this is the time of excuse and need.”
With regard to your saying, ‘I think it is better to pray two rak’ahs only rather than not praying at all’; then this is not true, because deliberately not fulfilling some pillars or conditions of the prayer makes it invalid, as we have already mentioned.
Allaah knows best.