Correct: Warum hältst du nicht an?
Why: Hälst du is the wrong conjugation! Hälst does not even exist. Look at the following conjugation of the verb halten (to hold, to stop):
Ich halte
Du hältst
Er/Sie hält
Wir halten
Ihr hält
Sie halten
Why is this mistake so common then among both German learners and Germans? It is largely due to its pronounciation. Hältst can very easily sound like hälst, especially if spoken quickly. Remember that when conjugating a verb, even if its stem changes radically or slightly (in this case the umlaut), it is the vowel that changes and hardly ever the consonant(s) in the stem So for halten, the stem is either halt or hält, as shown above.
