Yes, but only four times. From the Personal Edition FAQs:
What is "Document Recovery" and when should I use it?
Please read carefully: Technically, every document is now saved with a user key -- information that ties that file to the file's creator. In Personal Edition, users can only open files that they have created.
We recognize that it may be necessary to install QlikView on a different computer (i.e. computer upgrade, replacement, etc.). In order to open documents created using the previous installation of QlikView, you will need to "recover" the files. Recovering files simply means that you are assigning an updated user key (old machine -> new machine) to these documents. When you recover a file, you are telling QlikView that you are moving this file to your new installation, and you will no longer be using it on your previous installation.
IMPORTANT: QlikView Personal Edition is limited to four recoveries per installation. When you recover a QlikView file created with a previous installation, it will apply your new user key to ALL documents created using the previous installation, not just that particular file.
DO NOT attempt to open QlikView files that you did not create (from the forums, created by a colleague, etc.) Doing so will use one of your remaining recovery attempts, and once you have exhausted all 4 of the attempts, you will no longer be able to access documents that you have created and, from that point on, you will only be able to create new documents using your current QlikView installation.