cohenner,
I am currently trying the trial version of PD7 and I have had the same problem as you but with even shorter files. When trying to burn 1920x1080 AVCDH to disc it gets stuck at 24% and will stay there for hours, but PD hasn't stopped responding because I can cancel the burn and it will respond to my request to cancel. I have also had it get stuck at other percents of completion besides 24%, but that percent has happened more than once so there must be something unique about it. The getting-stuck problem has only has happened when I try to burn more than about 10 minutes of video to AVCHD on regular DVD-+R. 10 minutes or less works good.
Also, I have been able to have PD 7 create standard DVD output to hard disc with longer output. 23 minutes is the longest I have tried and it worked fine. It doesn't get stuck when creating standard DVD output from AVCHD files.
To this point I have suspected that the problem of getting stuck on AVCHD output it is because my PC is under-powered for AVCHD (Pentium 4 3.2 GHz --- planning to upgrade to a quad-core soon.)
I sent an e-mail to support asking whether an under-powered PC could cause this problem, or if it should work OK but would just take a very long time. However, I got back a form letter type of reply with a list of things to check on my PC, so they didn't really answer the question.
By the way, other than that one instance of getting a form-letter reply that didn't address my question, I have found Cyberlink's e-mail support to be excellent. Unlike many companies, they have actually answered my questions and have done so in a timely manner. And to be fair, when I got the form-letter type reply, it provided an opportunity to say whether my question was answered to my satisfaction, and a link to ask a follow up question. I didn't do that, figuring I will wait to see if a PC upgrade solves the problem before I take up too much of support's time when I know my PC doesn't meet their minimum specs for AVCHD.