The end of the first musical phrase has a descent:
In the first verse, the text sung to this phrase is "Abide with me, fast falls the eventide." As "the eventide" falls in the text, so does the melody in the tune. To some degree, this same feature applies to the fourth verse, the first line of which is "Swift to its close ebbs out life's little day." The line doesn't specifically mention a descent, but there's something of a connection between the musical descent and the "ebb[ing] out."
The end of the second musical phrase ascends:
I think only the sixth verse has lyrics that have added meaning when sung to this phrase. The second line there is "Shine through the gloom, and point me to the skies." The melody to which "to the skies" is sung ascends, as if the music itself is looking to the sky.
