I have received two logs ( thank you!) and they show that something on the system tries to launch BTT while it is already running.
I have no idea what that could be (and unfortunately I don't know of any way to find the calling process). But for now I have added a hidden setting that disables showing the preferences window when that happens.
You need to install v3.532 alpha (get via check for alpha version updates)
Then execute the following terminal command while BTT is quit:
defaults write com.hegenberg.BetterTouchTool BTTDontShowPrefsOnReopen YES