R. Yosef Yedid (Yeme Yosef §9) discusses the permissibility of a talmid chacham (i.e. an individual who sits all day and learns) or Torah-teachers refraining from fasting. From his responsum it appears he would also permit an employee [of secular occupation] to refrain from fasting since the unproductiveness amounts to stealing. As precedent he turns to Berachos 16a which states that workers do not recite all rabbinically required blessings [since they are hired workers].
However, I am unaware of other poskim permitting so lechatchila. In fact, R. Ovadiah Yosef (Chazon Ovadiah - Bein HaMezarim pp. 43-44.) strongly disagrees with R. Yedid, stating “it’s bewildering to say that all workers and clerks would be exempt from a public-fast”. While some indication to an exemption on the part of workers can be construed from the Yerushalmi (Demai 7:3), ROY asserts that that is only in a case of a personal-fast. ROY further adds that in contemporary times employers are not strict in these matters (essentially forgiving the couple of extra minutes) and therefore all workers are obligated to recite all benedictions upon finishing a meal (cf. SA 191:2).
Yet, it is still important to note that this can’t be a sweeping pronouncement or prohibition since other factors need be taken into account: What if the employer is a non-Jew and there likely is no “אדעתא דהכי” as assumed in the aforementioned SA? Employers are aware that many an employee has a drunken weekend, they might be lax on an added coffee-break the following work-day but would they tolerate a full unproductive day? Is there really no possible concern of “stealing” when, for example, a traveling salesman has a customer to which the employee must fly to and on account of his fasting he is unable to perform after the employer already spent money on the flight and lodge?
In short: People’s livelihood can be literally at stake when fasting. My -obviously theoretic- solution: If a person knows they will not be able to perform at work if they fast it is best to eat/drink within the minimum amount (cf. Beur Halachah 554:6) so A) they won’t fall ill [and consequently a bedieved case] and B) the fast won’t be considered broken. Suggestion: Choose your food and drink wisely.