You are correct in that "the prince was searching...." is past continuous tense and implies that the search is still going on from the perspective of the writer/speaker.
However, "the prince had been searching for ten hours..." (which is past perfect progressive tense) does not necessarily mean he has stopped searching either.
The prince had been searching for ten hours when he gave up.
This specifies that the search ended after ten hours, so the search is over.
The prince had been searching for ten hours when he began to lose hope.
This only says that he began to lose hope, not that he stopped searching. It points to an event that occurred (his giving it hope) and it is that which occurred in the past.