Yes, you can stay until the last match is played on the grounds. It's often the most fun, at night on the outer courts. Sometimes the matches out there go to late into the night.
Another note: if there's a match you're particularly interested in that's in the main stadium, go up to an usher in a better section, and ask him in a subtle way if there's any way a seat could be arranged for you there. I've always done this without any problem. Usually it's a $20 bribe. I felt nervous when I did this initially, but it's pretty standard, considering how many empty seats there always are. So if you feel comfortable..