When Did Hayek Renounce Liquidationism?

The short answer is: at some point after 1933. Certainly by the time of his 1937 essay “The Gold Problem” (“Das Goldproblem”; see Hayek 1999: 169–185, and 184), Hayek is found endorsing public works as a response to depression:

“Even though there are many concerns about organizing public works ad hoc during a depression, everything speaks in favour of having public agencies perform during a depression whatever investment activities need to be carried out in any case and can possibly be postposed until then. It is the timing of these expenses that presents a problem, since funds are often extremely hard to raise in the midst of a severe depression and the accumulation of reserves in good times generally faces the objections mentioned above. There is little question that in times of general unemployment the state must intervene to mitigate genuine hardship either by disbursing unemployment compensation or, as in earlier times, by legislation to help the poor." 
(Hayek 1999 [1937]: 184; see also Hayek 1978: 210–212).

Ludwig Lachmann in an Austrian Economics Newsletter (AEN) interview explains the change in Hayek’s thinking:

AEN: In the early 30’s there had been great interest among the profession in the ‘Austrian’ or Hayekian theory of the trade cycle. Yet as the 1930’s progressed even those who had been adherents seemed to have given up their belief in its correctness. What reasons do you think were behind this?

Lachmann: Well, you presumably know about the two different letters to the London Times that appeared in October, 1932. This, of course, was before I came to London. In one of them, Keynes and some Cambridge economists who were not, in general, his friends, like Pigou and Dennis Robertson, demanded that the government should take steps against unemployment. And three days later, Hayek, Robbins and Arnold Plant sent another letter saying that anything the government did by way of public works or similar methods would only make things worse and would not have the affect that Keynes claimed it would have.

That is to say, the ‘Austrians’ seemed to be committed to a policy of continuous deflation whatever happened. Yes, I’m quite sure that the apparent insistence of the ‘Austrians’ that the depression must run its course in the sense that both prices and wages in general must fall seemed to make it increasingly difficult for most other economists to support it, because it was by then obvious that wages didn’t fall, not in the Britain of the 1930’s anyway. That is to say, there was an obvious difference between the point of view expressed by Hayek, Robbins and their letter of October, 1932, and their willingness to admit the following year that a secondary depression was possible.

Ludwig Lachmann, “An Interview with Ludwig Lachmann,”The Austrian Economics Newsletter, Volume 1, Number 3 (Fall 1978), Mises.org.