In your example ....he settled permanently in America, where his work continued uninterrupted for the next twenty years.
We use uninterrupted because it was his work that was uninterrupted.
You could use uninterruptedly like this:
....he settled permanently in America, where he continued to work uninterruptedly for the next twenty years.
In the second case uninterruptedly describes how the work continued.
Student or Learner