The last two lines of this poem are the turning point, and make it all come together. Coleridge writes, "Work without hope draws nectar in a sieve, And hope without an object cannot live." [1.] The man is saying that drawing nectar in a sieve is impossible because is [sic] [it] just drains through, as will any work without hope. [End of 1.] Hope cannot live without an object, because if there is no hope and no point, then there is no reason to continue. These lines show how hopeless the man is. He has no hope, and sees himself as a cold, lonely winter. Although it is a beautiful day, blooming with the first signs of spring, he cannot see anything other than the hopelessness that surrounds him.
I have never sieved nectar, but gravity should cause any (viscous) liquid to permeate a sieve without needing human work? So I do not understand 1 above, even after reading the above explication.