The most common and most likely answer to this crossword clue is the 11 letter word MELANCHOLIC
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More clues leading to the result MELANCHOLIC
Buddy explains!

The straight part
We know that "Habitually dejected" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case habitually dejected = melancholic.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MELANCHOLIC mean?
MELANCHOLIC noun- A person who is habitually melancholy.
- Filled with or affected by melancholy—great sadness or depression, especially of a thoughtful or introspective nature.