Yes. He must resign. If he is not, The BJP should force him to resign, Even at the cost of making it 5 BJP ruled states from the current 6.
Reasons are -
1. He is neck deep in corruption charges. Him continuing at the helm will harm the image being projected by BJP for themselves.
2. The Reddys - Even if BSY does not resign, they will continue to do what they have done one month ago.
3. BSY seems to be threatening to pull down the government if he is removed. If a leader becomes larger than the organization, it is a sign of week organization and BJP would certainly does not want this image.
4. The Margins - the Government is surviving on laser thin margin and sooner or later this will fall for sure.
5. The only thing which may be holding BJP top brass is that he is very popular Lingayat leader, and his largesse to the Mutts from the public funds has made him stronger. this has helped BJP also as a Pro- right wing party. Removing him will be harming both these notions.
In view of the above, there are more cons than pros for BJP to continue with BSY.