[DoctorDulitlBest]

I had asked Mufti AbuHajirah this same question once. He said no.
One can pray tahajjud anytime after isha till fajr. But certainly the are times when tahajjud has more reward.
I think its in the earlier part of the last one-third of the night. Someone please confirm.

Asalaam u Alaikum,
See these links for more info:

http://www.askimam.org/public/question_detail/18254
http://qa.sunnipath.com/issue_view.a...ID=1241&CATE=4

In a nutshell

"Tahajjud Salaah begins after half the night has passed; whether one sleeps or not, Tahajjud Salaah can be performed. Sleeping is not a condition for the validity of Tahajjud. This is the accepted opinion. However, it is better to sleep and thereafter to rise and perform the Tahajjud Salaah.

Ml. Zakariyya bin Ahmed,
Student Darul Iftaa

Checked and Approved by:
Mufti Ebrahim Desai
Darul Iftaa, Madrassah In'aamiyyah