Pigeon in tree

Hello for the last week or so there has been a pigeon continually sitting in our olive tree.  There has been a very scant nest there since last year but this poor bird never leaves the nest and is starting to worry me.  I'm wondering whether it is ill or sad as it never eats or moves from the nest - ever.  There doesn't appear to be another pigeon around, so I doubt there will be eggs in the nest.  Please can somebody give me some advice.

many thanks