The $54 billion lifeline won by Credit Suisse Group on Thursday gives it a fighting chance to rebuild its business, but some clients aren’t waiting around to find out how that goes.

In Asia, several ultrawealthy clients continued to cut back their exposure amid the tumult this week. In the Middle East, some customers asked the bank to convert cash deposits into treasury bills and bonds. And in Germany, a wealth manager received inquiries from Credit Suisse clients looking to shift deposits to his firm.

Such attrition, if widespread, will make the overhaul that Chief Executive Officer Ulrich Koerner and his team are overseeing that much harder. Stemming the months-long exit of clients is critical to righting the battered Swiss bank, which saw net outflows hit 110.5 billion francs ($119 billion) in the fourth quarter.