All data which you add to AllMyPDFs will be immediately automatically saved. Therefore, AllMyPDFs has created a database on first launch. You find the database in the ~/Library/Application Support/AllMyPDFs/ directory. (The tilde here stands for your own user directory.)
Under Mac OS X 10.8, the path has been changed by Apple! Now you find the database in the directory ~/Library/Containers/net.dsd.AllMyPDFs/Data/Library/Application Support/AllMyPDFs/.
Even though we have tested each and every feature of the application, we cannot assure that your database may get damaged somewhen, for any reason. In this case, AllMyPDFs will probably behave very strange and either directly crash or be merely usable.
We presume that you use Time Machine or another backup system to protect your data. In this rare case, you should firstly try and restore your database directory (see above) from the last backup. If this doesn't help and you use Time Machine or another incremental backup system (with multiple backup versions), try the previous backup version.
If even restoring older backup versions doesn't help, you will probably have to bite the bullet and delete the complete database directory. Then AllMyPDFs can be launched and used again.