First I can't imagine any of the polymaths simultanenously working day to day at a deep level across multiple fields. We don't seem to be able to multitask that well.
However, I have a theory (so take with a grain of salt) that when we focus strongly on a task our brains rewire our neurons to optimise to use particular patterns for that situation. When you switch to a different field or spend time on a hobby your brain switches again as the previous patterns may not apply. It seems the breakthroughs come when the patterns from one field do apply to the new one. You may have been working on it forever but it took that change and the rewire to properly see it differently.