I am so sick of completeing surveys that don't open in new windows, and having no way of getting back to Turk to close out the survey after it is finished. Therefore, that HIT just shows up as abandoned. I've learned to ALWAYS make sure a new window is open for a survey before even accepting a HIT, unless otherwise prohibited.
You can right click on the link, and open it in a new tab, or you can go to the HITs assigned to you page, located under the HITs tab of the mTurk header. I always open surveys in a new tab, because sometimes they show up within the HIT frame.
All you have to do it click on the "Hits" tab at the top of the page and then click on "hits assigned to you" and then go to the hit you are looking for. Also just right click on the link and click "open in new tab" will assure that you get a new tab.