I wonder if there is any difference in the meaning between "1" and "2".
1. Don't leave your baby to cry.
2. Don't leave your baby crying.
Both sentences work, but I prefer the second one in this instance. However, there are times when the infinitive is preferable. Consider the following example:
"Don't leave that prisoner to rot."
"Don't leave that prisoner rotting."
In this case, the first sentence is the most natural sounding choice.