I think there is a misconception that the WTS would stop asking for donations if they felt that the recent amount was sufficient. That's not how it works. They ask for donations and support whether the money is pouring in or trickling in. Also, they would not want to dip into any savings if they can help it. The more urgent requests for money would not start when the savings are low. They would start when they are first having to use their savings, no matter how large those may be.
Like any business, they measure financial health based on current revenue and expenses. Your savings are there to get you through a tough period, but the goal is always to have positive net income. If the GB are placing emphasis on donations, it's because margins are thin or negative. They aren't going to wait for the money to run out before they ring the alarm bell.