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 majority of the Muslim scholars are of the opinion that repeating the words of the Athaan with the caller is desirable but not an obligation. The Hanafi School of jurisprudence and those who deny analogy are of the opinion that repeating the words of the Athaan is obligatory. They based their opinion on the Hadeeth that the Prophet said: "When you listen to the Muaththin (the person calling the Athaan), you should say exactly what he says." [Muslim]
The author of Awn al-Ma'bood wrote: "The evidence for the majority of the Muslim scholars is the Hadith reported by Imam Muslim and others that once the Prophet heard the Muaththin saying: "Allaahu Akbar (Allah is The Greatest), the Prophet said: "He is following the Fitrah." And when he said: "I testify that there is no true God but Allaah". The Prophet said: "He has come out of the Fire (Hell)." Since, the Prophet did not repeat the words of the Athaan, then this proves that repeating the words of the Athaan is desirable [and not obligatory]."
The Muslim scholars have different opinions concerning the matter of repeating the Athaan many times if it is called from many mosques. Some of them hold the opinion that one should repeat it whenever he hears it, while others believe that it is sufficient to repeat it only one time following the first Muaththin.
Hence, this is a flexible matter, if you wish you may repeat the Athaan only once, or you may repeat it with every Athaan to get more reward. According to the majority of Muslim scholars, if one does not repeat the Athaan at all, he does not commit a sin. Moreover, you should know that repeating the Athaan does not require you stopping your work. You may repeat the Athaan while performing your job.
For more benefit, please refer to Fataawa 104744, 92196 and 92707.
Allaah Knows best.