There seems to be a bug introduced in the 1.2.4 version: when doing anything that involves navigating through your directories - opening/saving/exporting/importing files - it does not seem to acknowledge double-tapping with your stylus to confirm. Workaround has to be using the Touchpad or keyboard.
I got my Aseprite from Humble Bundle and previously was using version 1.1.13, where the issue does not occur.
I use the Surface Pro 3 with a touch cover, and am on Windows 8.1 64x.