A few days ago we released LanguageTool 1.6. The error detection rules for a lot of languages have been updated and a few small bugs have been fixed. Feel free to use this forum to tell us how the release works for you.
One new 1.6 feature for the English language is the ability to detect "if three successive sentences begin with the same word". I have tested this feature using your online demo and it seems to work just fine.
However, when I test this same feature using the 1.6 add-on in LibreOffice, it does not work. I know that the Language Tool extension is working, because the following sentence is flagged as incorrect by LT:
I is a college graduate!
On the other hand, LT 1.6 does not flag the following sentence when installed in LibreOffice:
Mike stole my wallet. Mike stole my lunch. Mike stole my car. Mike is no friend of mine!
It's actually a known bug. Sorry we missed to make this clear in the changelog.