Yes, a christian can get depressed. Elijah in the Old Testament is one of the best examples. He had one of the most important spiritual achievement in turning Israel from Baal worship to the real God, Jehovah. But when Jezebel had sent him the letter mentioning that he will be killed, Elijah fled for his life. He was depressed after the long journey. Then He asked God to take his life. He was depressed.
But God gave him proper rest and food and renewed him.
Similarly sometimes we also feel depressed. Sometimes its because the devil accusing us of wrong things, sometimes bringing to remembrance our past sins, sometimes making us feel that we are good for nothing and useless.
But then how to handle the depressing situation?