Keynes is famous for saying: "In the long run we are all dead". How long is the long run? In other words, how long are you willing to wait for inflation to ease or for unemployment to improve?
When Keynes said this, he was critiquing the position taken by classical economists who say that the economy will repair itself in the long term. Keynes was arguing that the long run was too long for the individuals who would have to suffer while the economy repaired itself.
The question of how long is too long depends very much on how we are doing as individuals. If I have a good job, but the economy as a whole is doing badly, I can wait a long time for unemployment to ease or for inflation to fall. However, if I am unemployed, even a few months are likely to be too long unless somehow the government is going to help me through the bad times.
The problem is that we shouldn’t necessarily base our policy on the desires of the people who are being hurt. What if the classical economists are right and our economy would be better off in the long run if we let some people remain unemployed? In that case, we would actually be hurting the economy if we let the government intervene and use Keynesian policies. It might be better for us to let the economy fix itself, particularly if we give unemployment benefits to those who are hurt by the changes in the economy.
To return to the main part of your question, though, I would say that 6 months would have to be the absolute longest that I would give the economy to turn itself around if I were one of the people who was unemployed.