I think minimum number of sign ons isn't good solution, because for cheater, who is programmer, it's easy to create automatic script, which monitors number of signs ons, signals necessity of logging in and prevents ban. Currently we are forced to log into BB at least once per 6 weeks, so this idea changes only period of time and nothing more. So I prefer to modify this idea in way, which isn't possible to bypass by script.
Therefore my idea is: Minimum number of open threads on suggestion forum.
Every user has to write, let's say, at least one suggestion every week (or day, or month - it's thing to discuss) on this forum. I hope it's final solution, which solves everything. I think in this way after few weeks BB would be game without cheaters.