Well, here is my experience with eSaver to share with you, as I have held this account and taken part in many rounds of this promo. I have also put in incremental funds and had to withdraw part of them for needs like yours. In 1 month, 1 transfer in, partial transfer out. The bonus interest is accessed on each day's balance and credited at the end of the month. Not once did I lose out on the bonus interest, and I counted it carefully.
Illustration:
1 Aug - put in $100k
16 Aug - take out $50k
31 Aug - you earn bonus interest for $100k x 15 days and $50k x 16 days
Maybe it is because it is clear enough for me that they are fresh funds i.e. I never transferred from or to another Stanchart account, but something else outside. I suppose if they want to be picky, they can argue about whether they are fresh funds, but it has been fine for me.