In my _personal_ experience, manic phases last 2 weeks to 2 months, followed by 4-10 months of catatonia.
It is approximately the same for my aunt and grandmother. In their cases, lithium and electroconvulsive therapy were the only things that work. For me, lamotrigine and modafinil are life-changing wonder drugs.
That said, people in my group therapy reported cycles as short as days to weeks - rapid cycling, as you say.
Note that the "off time" need not be matched by a depressive episode (and in fact I find that unlikely, since depression is not very restful) -- it could simply be exhaustion hiding the symptoms of the underlying (long) manic episode.
Consider that it's "just" a mood disorder, where mood management can be affected by random stimuli. So, their mood might be stable until some stimulus comes by. And that stimulus could just be a random memory, which can create a feedback loop. It's "fun".