Salah of Tasaabeeh (i.e. Extolments) should not be prayed at prohibited times
14-1-2014 | IslamWeb
Question:
Can the Salaah of Tasaabeeh be Performed after the ‘Asr Prayer?
Answer:
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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The majority of Muslim scholars agreed that it is disliked to perform voluntary prayers after the ‘Asr prayer. Abu Sa‘eed Al-Khudri 
narrated that he heard the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, say: "There is no prayer after Fajr (dawn) until the sun rises and there is no prayer after ‘Asr until the sun sets."
The Salah of Tasaabeeh is not among the prayers that are performed for a specific reason so it should not be performed at times when prayers are prohibited. Voluntary prayers that are done for a specific reason are permitted to be prayed after the ‘Asr prayer.
Umm Salamah 
said, "The Messenger of Allaah, sallallaahu ‘alayhi wa sallam, offered the ‘Asr prayer and then performed two Rak‘ahs. I asked him about this and he, sallallaahu ‘alayhi wa sallam, answered: "O daughter of Abu Umayyah (i.e. Umm Salamah), you were asking me about these two Rak‘ahs after the ‘Asr prayer. Some people from the tribe of ‘Abd Qays came to me (to embrace Islam) and busied me so much that I did not offer the two Rak‘ahs which were to be offered after the Thuhr prayer. These two Rak‘ahs (you have seen me offering) make up for those." [Al-Bukhari and Muslim]