You don't say how many segments you have already travelled, nor if the ticket was originally issued before July 1st 2007.
Assuming the ticket was originally issued after June 30th 2007, you are entitled to a maximum of 20 segments, flight & surface combined.
From pre-June 1st Starfile:
2N FLIGHT SEGMENTS
3N ----------------
4N .
5N . 1. 3 SEGMENT MINIMUM REQUIRED
6N . 2. 20 SEGMENT MAXIMUM PERMITTED, INCLUDING
7N . SURFACE SEGMENTS* AND FREE/PURCHASED FLIGHT
8N . SEGMENTS FOR THIS FARE.
9N . *SURFACE SEGMENTS NOT COUNTED AS SEGMENTS FOR
10N . TICKETS ISSUED PRIOR TO 01JUL07
snip
2N CHANGES
3N --------
4N .
5N PRIOR TO DEPARTURE
6N . snip
30N .
31N AFTER DEPARTURE:
32N TRAVEL ORIGINATING AREA 1/2/3
33N .
34N . 1. DATE/TIME AND ONEWORLD CARRIER CHANGES ARE
35N . PERMITTED WITHOUT REISSUE PROVIDED ORIGIN,
36N . DESTINATION, CONNECTING POINTS AND INVENTORY
37N . REMAIN THE SAME.
38N . 2. ROUTING CHANGES OTHER THAN DATE/TIME AND
39N . ONEWORLD CARRIER PERMITTED AT A CHARGE OF
40N . USD125.00 PER TRANSACTION. CHILD/INFANT DISCOUNT
41N . DOES NOT APPLY.
51N LOCAL SERVICE FEES MAY APPLY.
IMHO, CX can only deny your reissue if it would take you beyond the segment limit or the maximum validity. If you would post your total itinerary as travelled, date of original ticket issue, & date of first flight (TPE-HKG) I'm sure it can be rapidly checked out.
Edit: June 1 2008 changes irrelevant - Ticket was bought last year.