You can leave your money in the stadium. But all you can do is to upgrade banks to hold more money or buy gear in the sports shop. Perhaps if your city isn't fully developed you might buy a plot of land.
the stadium has no limit to what it can hold.. just wait till you get a builder freed up and spend what you have on you.. then hit up the stadium.. you wont lose it as long as you do it before the end of the season... I'm pretty sure i remember reading that they made a change some time ago and $ will not roll over now.. But i could be wrong about that part