As far as i know there is no time limit to start part 2.
I finished part 1 in july 2012 and did not buy the assignment voucher until Nov 27th 2012.
I downlaoded the assignment on Dec 4th, that gave me until jun 4th to upload the assignment and essay.
Please note, you get 6 mnths from assignment dowload to complete both the assignment and essay.
SCJP 5.0, SCBCD 5.0
Working towards OCMJEA, cleared part 1,2 and 3. Yet to attend training