There has to be a way to fix it, else every website would whitescreen like that.
The good thing about MySQL is that it supports connection pooling (a quick Google search taught me that), and that it would cut down on the whitescreens if it were in use, as it helps with database applications such as this.
However, I never learned server programming, so I don't have that much experience with this kind of thing. Hey, for all I know, it's in use now. But this still shouldn't be happening. And it happens regularly! Someone needs to sit down and fix this.