Thanks for using OnSong!
OnSong uses the built-in viewer component from Apple to display PDF files. This issue occurs when the device is running low on working memory. This is especially apparent on older devices like the iPad 1 and iPad 2 that have less than 1 GB of RAM. Newer versions of iOS do not handle low memory issues when display PDF files gracefully which results in the screen going blank.
Please try going into the Utilities menu (gear icon) --> Settings --> Display Settings --> Song Viewer --> Renderer Version and set that to "New" and tap Done.
http://onsongapp.com/docs/interface/menubar/utilities-menu/settings/display-settings/song-viewer/
That will use a more conservative method for displaying PDF files that may avoid blank pages due to memory issues.
Hope that helps!