The in app update process is broken when updating from TaskPaper 3.3. The problem is that I changed TaskPaper’s bundle identifier in later version, and that makes the in app update process think that there’s a security problem, and it stops the in app update.
Instead move the old 3.3 version to the trash. Download the latest version directly from www.taskpaper.com and install it. This is a free update, if you are prompted for a license key by the new version just enter your same 3.3 license key.
Sorry for the trouble! The in app update process should once again work for versions greater then 3.3.