The scholars of Islam insist that a Muslim must not deliberately delay the performance of the five mandatory prayers beyond their specified time.
But if we forget to do them owing to reasons beyond our control or have fallen asleep, there is no blame. But then we should perform them as soon as we remember or wake up.
Islam permits no excuse for the deliberate postponement of prayer owing to work or business or study or any other worldly pursuit.
Indeed one of the characteristics of genuine believers is that they do not permit any worldly affairs to take precedence over the observance of regular prayer within the specified time.
Allah in His Noble Quran describes the believers thus:
People whom neither [worldly] commerce nor striving after gain can divert from the remembrance of God, and from constancy in prayer, and from charity: [people] who are filled with fear [at the thought] of the Day On which all hearts and eyes will be convulsed [and who only hope] that God may reward them in accordance with the best that they ever did, and give them, out of His bounty, more [than they deserve]: for, God grants sustenance unto whom He wills, beyond all reckoning. (Quran 24:37, 38)
People who are engaged in trade or business are generally unwilling to pause their activities for a while for anything; they think they will be losers if they do so. They forget that Allah is the Disposer of all affairs, and without His blessing no human activity can bear fruit.
So the best we can do is to plan our activities in such a way that we set apart short intervals in the midst of our activities for prayer, which need not take more than a few minutes.
Allah Almighty also says of later generations of people who ignored their prayers:
Yet they were succeeded by generations [of people] who lost all [thought of] prayer and followed [but] their own lusts; and these will, in time, meet with utter disillusion… (Quran 19:59)
On the basis of the Quran and the Sunnah, our jurists have clearly specified the time for each Salah, for which there is a beginning time and no one is expected to perform it before that time. And for each prayer there is an ending time too, after which no one can do it with the certainty of acceptance by Allah.
We should not postpone the mandatory five times’ Salah, not even during the times of battle, fear, or illness.
Even a person suffering from an extreme illness is not exempted from prayer. Such a person is allowed to pray sitting if difficult to do it standing; and if he or she can’t do it sitting, they can do it lying on bed.
And if a patient can’t make wudhu (ablution), they can do tayammum (a form of ablution without using water) before the prayer. All these underscore the fact that Salah cannot be postponed for the sake of some worldly pursuit.
The foregoing means that study, research or project work is NOT a valid excuse for the postponement of prayer.
Breaks in Work Are Good, Not Bad
Now let us come specifically to your problem, namely your fear that if you stop in the middle of your work for prayer, you will lose your focus. You feel, effectively, that you can’t engage in any meaningful work or project if you take an interval or recess for prayer.
In fact, several studies have been conducted about the advantages or disadvantages of taking a break from work; and these show that taking an interval actually enhances creativity.
A recess from any difficult work or project allows the person to take up the work with a fresh mind and approach after the break which allows them to view the problems in a new light. This reinvigorates their creative potential to produce much better results than they could otherwise achieve.
Your feeling that taking a recess is detrimental to your creative efforts is a misunderstanding about how your brain works.
Allah Knows Best What Is Good
Allah is Wise and He knows about the strengths and weaknesses of humans; and the five times’ mandatory prayers have indeed more benefits than we can easily see or assess at face value.
We need Allah’s help and guidance in matters where we encounter difficulties or where we are utterly helpless. The best way to get His help and guidance is to supplicate to Him, and one of the best times for supplication is just after our mandatory prayers.
And if by any chance you miss a prayer, you need to do it before performing the next one. Also you need to ask the forgiveness of Allah Almighty to forgive you for your lapse in the doing of the mandatory prayer.
Finally it all depends on your faith in Allah Almighty and your commitment to live in submission to His will. And Allah knows best.