Can the same soorah be repeated in prayer?

There is nothing wrong with repeating the same soorah in
Taraweeh prayer, or in any other prayer. A person may recite a soorah in
the first rak’ah and repeat the same soorah in the second. The evidence
for that is the general meaning of the verse in which Allaah says
(interpretation of the meaning): 

“Verily, your Lord knows
that you do stand (to pray at night) a little less than two thirds of the
night, or half the night, or a third of the night, and also a party of those
with you. And Allaah measures the night and the day. He knows that you are
unable to pray the whole night, so He has turned to you (in mercy). So,
recite you of the Qur’aan as much as may be easy for you”
[al-Muzzammil 73:20] 

Abu Dawood narrated (816) from Mu’aadh ibn ‘Abd-Allaah
al-Juhani that a man from Juhaynah told him that he heard the Prophet
(peace and blessings of Allaah be upon him) reciting Idha zulzilat al-ard
[al-Zalzalah 99] in both rak’ahs of Fajr prayer and (he said) I do not know
whether the Messenger of Allaah (peace and blessings of Allaah be upon
him) forgot or he recited that deliberately. This report was classed as
hasan by al-Albaani in Saheeh Abi Dawood. 

‘Abd al-‘Azeem Abaadi said: 

The Sahaabah were
uncertain as to whether the Prophet (peace and blessings of Allaah be
upon him) repeated the soorah because he forgot, as it was his habit to
recite a different soorah in the second rak’ah to what he had recited in the
first, so that was not prescribed for his ummah, or he did it deliberately
to show that it is permissible. So it is uncertain as to whether it is
permissible to repeat a soorah or not. If it is not clear whether it is
permissible or not, then it is more appropriate to interpret what the
Prophet (peace and blessings of Allaah be upon him) did as meaning that
it is permissible, because the basic principle concerning his actions is
that they were done to show what is prescribed, and the idea that he forgot
goes against that principle. 

‘Awn al-Ma’bood, 3/23 

Indeed, there is nothing wrong with repeating a soorah or a
verse within the same rak’ah. 

Al-Nasaa’i (1010) and
Ibn Maajah (1350) narrated that Abu Dharr (may Allaah be pleased with him)
said: The Prophet (peace and blessings of Allaah be upon him) stood
reciting a verse and repeating it until morning came. That verse was: “If
You punish them, they are Your slaves, and if You forgive them, verily, You,
only You, are the All‑Mighty, the All‑Wise” [al-Maa’idah 5:118]. Classed
as hasan by al-Albaani in Saheeh al-Nasaa’i. 

Al-Bukhaari (5014) narrated from Abu Sa’eed al-Khudri that a
man heard another man reciting “Qul Huwa Allaahu Ahad (Say (O Muhammad):
He is Allaah, (the) One)” [al-Ikhlaas 114] and repeating it. The next
day he came to the Messenger of Allaah (peace and blessings of Allaah
be upon him) and told him about that, and it was as if the man did not think
much of that. The Messenger of Allaah (peace and blessings of Allaah be
upon him) said: “By the One in Whose hand is my soul, it is equivalent to
one-third of the Qur’aan.”  

According to another report: A man stood at the time of the
Prophet (peace and blessings of Allaah be upon him) reciting “Qul
Huwa Allaahu Ahad (Say (O Muhammad): He is Allaah, (the) One)” [al-Ikhlaas
114] at the end of the night, and he did not do more than that, but the
Messenger (peace and blessings of Allaah be upon him) approved of his
repeating the same soorah. 

Al-Haafiz said: 

The one who recited it was Qataadah ibn al-Nu’maan. Ahmad
narrated via Abu’l-Haytham that Abu Sa’eed said: Qataadah ibn al-Nu’maan
stayed up for the whole night, reciting “Qul Huwa Allaahu Ahad (Say (O
Muhammad): He is Allaah, (the) One)” [al-Ikhlaas 114] and he did not
recite anything else…. And al-Daaraqutni narrated another version of this
hadeeth via Ishaaq ibn al-Tabbaa’ from Maalik, in which it says: “I had a
neighbour who would spend the night in prayer and would not recite anything
other than “Qul Huwa Allaahu Ahad (Say (O Muhammad): He is Allaah, (the)
One)” [al-Ikhlaas 114]. End quote. 

We ask Allaah to enable you to memorize His Book, and to act
upon it. 

And Allaah knows best.