All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Yes, it is permitted to repeat the recitation of Al-Ikhlaas Soorah [Quran 112] in Tahajjud prayer because it is proved in a Hadeeth that 'Aa’ishah said: “The Prophet spent one night in Qiyaam al-Layl (optional prayer at night) reciting one verse of the Quran.” [At-Tirmithi]
Other narrations of the above-mentioned Hadeeth state that that verse is the saying of Allah (which means): {If You should punish them - indeed they are Your servants; but if You forgive them - indeed it is You who is the Exalted in Might, the Wise.} [Quran 5: 118]
However, the Prophet did not take such an action as a habit. So, one is advised not to stick to it unless he has not learnt by heart any other verse or Soorah.
For more benefit on how to perform the Tahajjud prayer, please refer to Fatwa 81337.
Allah knows best.