I thought Elie's letter states the rationale quite clearly:
I understand their concerns and agree with them that it is crucial that GiveWell has a board that plays a serious role in its governance. After discussing alternative board constructions with staff, current GiveWell board members, and my counterparts at other nonprofits, I believe that the direction we have chosen (which means a smaller board for now) is the right one for GiveWell. In a nutshell, I believe it will mean a more focused, intensely engaged board, and ultimately a more robust, more impactful GiveWell. I recognize there is room for disagreement on this point, and the board will continue to revisit this decision over the coming years. We will expand in the future if we believe doing so will help us further GiveWell’s mission most effectively.
Seems like Givewell had a sense that the current board was large, and this made it harder for the board to serve its function, so they decided to reduce it in size.
GiveWell recently published the recording from its April 2019 board meeting.
I was holding that this meeting would include discussion of why the members resigned, but I was mistaken.
It seems that Rob Reich, Brigid Slipka, and Tom Rutledge resigned before this meeting, then at the meeting the board voted to formally reduce the number of board seats.
So I'm not sure that there is any publicly available discussion of these resignations, apart from the statements GiveWell published in April.
(I haven't listened to the end of the recording yet; from the way the conversation is headed it doesn't sound like there's going to be any further discussion about the resignations or board size. Edit: I listened to the rest of the recording and this wasn't discussed.)