God did provide food and drink (see for example 17:6 but also 17:7, 17:8-16; 18:41-46).
And, once again, when Elijah is running away from a death threat by the king, the Lord has provided food and water sufficient for him to keep on his journey.
But, now, Elijah is in despair. He had done everything that God wanted; yet, his enemies want to kill him. He ready to give up, to die.
God comes to him in his despair.
Comes to him in an unexpected way. Comes to him in silence.
The commentary in The New Interpreter's Study Bible points out what a contrast this is from earlier theophanies which were accompanied by fire, wind, thunder, lightning, and earthquakes, such as in Judges 5:4-5; Psalms 18:7-15; 68:7-8; Habakkuk 3:15.
In an unexpected way, but Elijah is able to recognize God's voice anyway.
When Elijah heard God's voice, he listened. And he did something else. He spoke. He spoke of his discontent. "I've done everything you told me to do, and the result is that they want to kill me. I'm the only one left."
What did Elijah expect God to say? What response do we expect when we lay our lamentations out? Remember, he's not just making this up--he really has been obedient, and people really are out to get him.
God tells him to anoint new kings for Aram and Israel and to anoint a new prophet, Elisha, to succeed him.
God is telling him, "I've haven't abandoned you, but you aren't to abandon your mission, either." Here's how Allen & Williamson put it in Preaching the Old Testament:
Responding to the call and claim of God is a risky busines, and defeat and despondency are often the companions of those who do so. We should not wallow in such feelings, although Elijah did just that, but be open to the God who ever call us forward as Elijah, in spite of himself, was called. God's adamant love gets us through the hard times.