Answer
Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If you pray Witr then you want to pray Qiyam al-Layl after that, you should pray it two by two, and you do not have to repeat Witr.
Responding to the question in point, Sheikh M. S. Al-Munajjid, a prominent Saudi Muslim lecturer and author, states:
“If the Muslim prays Witr then he wants to pray Qiyam al-Layl after that, he should pray it two by two, and he does not have to repeat Witr.
The Prophet (peace and blessings be upon him) commanded that the last prayer offered at night should be Witr, but this command is in the sense that it is mustahabb (recommendable), not obligatory.
Sheikh Ibn Baaz was asked:
If I have prayed Witr at the beginning of the night, then I get up to pray Qiyam at the end of the night, how should I pray?
He replied:
If you have prayed Witr at the beginning of the night then Allah enables you to get up at the end of the night, then pray whatever you can two by two – without Witr, because the Prophet (peace and blessings be upon him) said: “There cannot be two Witrs in one night.”
And it was narrated from Aishah (may Allah be pleased with her) that the Prophet (peace and blessings be upon him) used to pray two rak`ahs after Witr sitting down. The reason for that – and Allah knows best – was to show the people that it is permissible to pray after Witr.”
Allah Almighty knows best.
Excerpted, with slight modifications, from: www.islamqa.info