Don't let me down.
(What is the part of speech of 'down' in this sentence? And what is the meaning of 'down' here?)
To let someone down is an idiom.
http://idioms.thefreedictionary.com/let+down
The word "down" is an adverb, and in this sense it's part of an idiom, too. The whole idiom means to disappoint.
You can find more help with phrasal verbs and idioms here:
http://www.eslcafe.com/students/