His work schedule prevents him from breaking his fast after Maghrib in Ramadan; is it permissible for him not to fast?

Fasting Ramadan is one of the five pillars of Islam, and every Muslim
should be keen to do it as Allah has commanded him, and he should not be
negligent concerning it or give worldly work precedence over it. If there
is a conflict with his worldly work and he is able to reconcile between
them, then he should do so, thus achieving what is in his best interests
both in this world and the hereafter. If he is not able to reconcile
between them, then he should not be heedless with regard to one of the
pillars of Islam and one of its greatest foundations, because of some
worldly concern. Rather he should give precedence to fasting, and he
should examine the worldly matter that conflicts with it. If he can reduce
that thing, then he should reduce it, and if he can change it, then he
should change it, even if it will bring a lower income, because the
hereafter is better and greater in reward. Whoever is eager and pays
attention to matters of his religion, Allah will suffice him in his
worldly affairs, as He, may He be glorified and exalted, says
(interpretation of the meaning):

“And whosoever fears Allah and keeps his duty to Him, He will
make a way for him to get out (from every difficulty).

3. And He will provide him from (sources) he never could
imagine”

[al-Talaaq 65:2-3]. 

Imam Ahmad (20215) narrated that one of the Companions of the Prophet
(blessings and peace of Allah be upon him) said: The Messenger of Allah
(blessings and peace of Allah be upon him) took hold of my hand and started
to teach me some of that which Allah, may He be blessed and exalted, had
taught him, and he said: “You will never give up something out of fear of
Allah, may He be glorified and exalted, but Allah will give you something
better than it.”

Classed as saheeh by al-Albaani in ad-Da‘eefah (1/62). 

Ibn Maajah (257) narrated from ‘Abdullah ibn Mas‘ood (may Allah be pleased
with him) that the Prophet (blessings and peace of Allah be upon him) said:
“Whoever focuses all his concerns on one issue, namely the Hereafter, Allah
will suffice him and spare him the worries of this world. But whoever has
many concerns about different worldly issues, Allah will not care which of
these worries will cause his death.”

Classed as hasan by al-Albaani in Saheeh Ibn Maajah (207) 

At-Tirmidhi (2465) narrated that Anas ibn Maalik (may Allah be pleased with
him) said: The Messenger of Allah (blessings and peace of Allah be upon him)
said: “Whoever is mainly concerned about the Hereafter, Allah will make him
feel independent of others and will make him focused and content, and his
worldly affairs will fall into place. But whoever is mainly concerned with
this world, Allah will make him feel in constant need of others and will
make him distracted and unfocused, and he will get nothing of this world
except what is decreed for him.”

Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi 

You should not give up fasting in Ramadan because of this invalid system of
rules or any other reason that is not regarded, according to Islamic
teaching, as a valid reason for not fasting. So it is not permissible for
you not to fast and to offer expiation by feeding the poor, because you are
able to fast. Rather offering expiation is a concession granted to those who
are unable to fast, such as those who are elderly and frail, or those who
have chronic sicknesses for which there is no hope of recovery. Allah, may
He be exalted, says (interpretation of the meaning):
“And
as for those who can fast with difficulty, (e.g. an old man, etc.), they
have (a choice either to fast or) to feed a Miskeen (poor person) (for every
day)” [al-Baqarah 2:184]. 

This refers to those who
found it burdensome and unbearably difficult, such as the elderly; they
could compensate by feeding one poor person for each day they did not fast.

Tafseer as-Sa‘di
(p. 86) 

Shaykh ‘Abdullah ibn Muhammad ibn Humayd and Shaykh ‘Abd al-‘Azeez ibn Baaz
(may Allah have mercy on them) said: 

The basic principle is that it is obligatory to fast Ramadan and to have the
intention to fast from the night before; this is required of all Muslims who
are accountable, and they should start the day fasting, except those to whom
the Lawgiver has granted a concession allowing them to start the day not
fasting. This refers to those who are sick or travelling, and others whose
situation is likened to theirs. Those who do hard work are included among
those who are accountable, and are not like those who are sick or
travelling. Therefore they are obliged to have the intention of fasting
Ramadan from the night before, and to start their day fasting; if any of
them is compelled to break his fast during the day, then it is permissible
for him to break the fast and eat or drink enough to ward off harm from
himself, then refrain from eating and drinking for the rest of that day,
which he should then make up at a suitable time. If a person does not
encounter such necessity, then he must continue fasting. This is what is
dictated by the shar‘i evidence from the Qur’an and Sunnah, and by the words
of the leading scholars of all madhhabs. End quote. 

Majmoo‘ Fataawa Ibn Baaz
(15/245-246) 

This man should submit to the administration of his work a request to be
exempted from this unfair rule, so that they will allow him to break his
fast at sunset, or schedule his work during the night. If they agree to
that, all well and good; otherwise he should look for another job that will
not cause him to neglect the fast. 

Whoever gives up something for the sake of Allah, Allah will compensate him
with something better than it. 

For more information, please see the answer to question no.
65803.

And Allah knows best.