Praise be to Allah, the Lord of the Worlds.
If a person travels (81 Km) or more from their hometown, for a legitimate purpose, then they are allowed to shorten and combine prayers until one of the following happens:
1-When he decides to stay in the city of arrival for an unlimited time, then he ceases to be a traveler, and so he isn`t allowed to shorten and combine prayers.
2-When he decides to stay in the city of arrival for four days or more, other than the day of arrival and that of departure, then he ceases to be a traveler once he arrives there. Therefore, he isn`t allowed to shorten and combine prayers. However, if decides to stay less than four days, other than the day of arrival and that of departure, then he is allowed to shorten and combine prayers.
3-If he decides to stay for three days, other than the day of arrival and that of departure, but had to extend his stay, then he ceases to be a traveler by the end of the third day. Therefore, he isn`t allowed to shorten and combine prayers after that day (Third).
4-If he doesn`t know exactly when his work will be done, but expected to finish it before the passage of four days, but that expectation was wrong and so he had to extend his stay, then he is allowed to shorten and combine prayers up to eighteen days.
The evidence for determining three days as the period during which a traveler is allowed to shorten and combine prayers is the following Hadith: Al-'Ala' b. al-Hadrami reported Allah's Messenger (PBUH) as saying:
"The Muhijir should stay at Mecca after performing the rituals (of Hajj) but for three (days) only."{Related by Bukhari & Muslim}. Scholars said, "It was prohibited for the Muhajireen to stay at Makkah and dwell with the disbelievers. As a concession, the three days indicate that a person is still on travel; whereas, the four indicate that he isn`t."
As for allowing the traveler to shorten and combine prayers up to eighteen days in case his work took more time than he had expected, this refers to the period through which the Prophet (PBUH) had shortened and combined prayers upon the conquest of Makkah. For further details, kindly refer to Moghni al-Mohtaaj, 1/519-521}. And Allah knows best.