I voted for 3 months. 6 months in my opinion is too long of a period for someone to be inactive and be expected to return. If someone has joined a forum, then it is their responsibility, not the forum's, to ensure they visit and participate as often as is needed to maintain membership. There are too many administrative duties involved with running a forum to give users that much time to figure out that they need to participate. All my opinion of course.
I would like to use that timeline (3 months) however, the problem is those who still want to be in the forum end up creating their account all over again and it can get either confusing or double the effort to welcome them back unnecessarily.
Maybe a warning should be given every time a user hasn't posted in a period of one month before he will be deleted, to give him an opportunity to come back and post. Then after three warnings given he could be deleted. Then the user will certainly have a chance to avoid deletion.
Since the beginning of this Community we have been actively deleting Members for not participating. We currently have one in progress, please make sure to read through the Newsletter: Newsletter - September 2017.