The beginning of greet with the Salam is a desirable Sunnah, and its response is a duty (Wagb) in unanimous.
If the two Muslims meet, and each of them greets over to the other, then if they go for a while and then met again - even close - it is better to greet one of the other, even if repeated repeatedly.
Evidence of this is what Abu Hurayrah said in Hadith:
1- Narrated Abu Hurayrah:
A man entered the mosque while Allah's Messenger (ﷺ) was sitting in
one side of the mosque. The man prayed, came, and greeted the Prophet.
Allah's Messenger (ﷺ) said to him, "Wa 'Alaikas Salam (returned his
greeting). Go back and pray as you have not prayed (properly)." The
man returned, repeated his prayer, came back and greeted the Prophet.
The Prophet (ﷺ) said, "Wa alaika-s-Salam (returned his greeting). Go
back and pray again as you have not prayed (properly)....."
(Narrated by "Bukhari" in his "Saheeh") 
2- And also Narrated Abu Hurayrah from the Prophet Muhammad said:
When one of you meets his brother, he should salute him, then if he
meets him again after a tree, wall or stone has come between them, he
should also salute him.
Grade: Sahih Mauquf and Marfu' (Al-Albani)
(Narrated by "Abi Dawud" in his "Sunan") 
This repetition is one of the things that are desirable (Sunnah), and it isn't one of the duties (Wagbat).
It's enough for peace for the first time, it brings the origin of the Sunnah, and there is nothing wrong with it, Insha Allah.
Especially if there is one who works or busy such as your case,
or in public places and the repetition of peace may let the people stop working every time to respond to him.
I hope my answer is clear.
And Allah knows best!
-  Sahih al-Bukhari (6251) - (Chapter: To reply a greeting saying, "Alaikas-Salam")
-  Sunan Abi-Dawud (5200) - (Chapter: Regarding when a man parts from another, then meets him again, he should greet him with the salam)
- Full answer in Arabic
- More info To reply a greeting saying, "Alaikas-Salam"