If/where should I explain the reason of my low BSc GPA in a PhD application?
You need a sentence or less to get this idea across. &quot;While illness affected my undergraduate performance, I overcame the issues as my MS performance demonstrates.&quot;
There are a lot of places for such a sentence depending on the application materials requested. Even the SOP might &quot;host&quot; it, provided that you make the SOP more about the future and your goals than about the past. But the personal statement, if required, is probably better. But a separate document might be rejected.
If you are required to provide letters of recommendation, make sure that the writers emphasize your current skills and ability to succeed. They don't need to mention the problems, but their impact should lead to the assumption that poor performance is not expected in future.
But having been rejected twice means little in the abstract. Perhaps they are just the wrong places for you. A broad approach (several institutions with varied reputations) is a better way to assure success than any narrowly focused program.