I'm assuming there is some algorithm involving rep, time maybe, maybe
The algorithm is deliberately secret to avoid gaming (e.g. living just on the edge of the ban) but what you need to do to lift the ban should be clear however; as described within What can I do when getting “We are no longer accepting questions/answers from this account”?. However the algorithm does not take time into account, it will only be lifted once posts improve or other positive contributions are made.
It also doesn't say whether one is notified or one just has to use
trial and error.
You need to attempt to ask a new question/answer. The state of the ban is checked when attempting to ask/answer
I have no idea of the effort involved in getting ban lifted and
whether it is worth while or not.
Likely considerable effort will be required but it depends how "deep" into the ban you are