In the first part of your quote "tired of being on the road," the road isn't necessarily literal. Often, the road represents a journey or a travel. The author might be tired of a physical travel, but it could also be a metaphorical travel. The author might be tired of a mental journey or a trying time in his/her life.
The second part of your quote, "lonely as a robin in the rain," leads me to believe the author is referring to a metaphorical travel. Rain often symbolizes the dark and difficult times in our lives. If we look at the literal side of this section, birds can't fly very well in the rain. The water adds weight and causes their wings to fail. A robin caught out in a rain storm without selter would probably be alone. The other birds and animals would have sought shelter. The author of this quote is saying that he/she is tired of being alone during a difficult time in their life.