I have a use case where if a website user has clicked on personalized offer served from target ( say a banner button) do not show him the offer for next 6 months, however after next 6 months the customer should again be eligible for that offer/audience.
Target cookie is valid only for maximum 90 days (depends on the cookie lifetime being configured for the account), you would not be able to track the customer within Target itself.
However, you can definitely stop displaying the activity to the customer once they have achieved the activity conversion which is clicking on the offer in this case. This can be done through advanced settings of the success metrics. (Increment count, release user, and bar the user from reentry). Please review below document for more information in this regard.>> Success metrics
For the second part, where you want to display the offer to the visitor again after 6 months. You may use a shared audience from Analytics. Once a user is a converter, you may pass a parameter like an event to Analytics. Then create a segment in Analytics to capture the visitors of the page after 6 months. This segment can further be used in Target activity for targetting visitors again.