From what I've seen and heard, some instructors WILL provide private lessons for a fee while many will NOT.
I think a common answer is that it is the dynamic of the group, working in class with a variety of partners, that one learns from (there is no one way something works on all people).
My question to you is: are you frustrated about one particular aspect that you feel you are slow with (for instance, your back roll really sucks, or you just can't figure out where to put your feet for tenkan)? If so, then asking the instructor or a senior student if they are willing to work with you for 15 minutes before or after a class may help.
A couple of other thoughts:
If you feel your progress is slow, well, the thing many of us find with aikido is that the process is everything (after 7 yrs I'm just beginning to feel I understand the ramifications of the simple turning exercise we call tai no henko); relax, breathe, take each class as it comes and don't worry about pace of "progress."
If you feel you have a learning style that is not met by the instructor's teaching style, that may need to be looked at. Some of us learn best by slowly parsing out the technique into tiny pieces, some of us have to have verbal instructions to follow along with, some of us have to stand next to the demonstrator and shadow the movements, etc.
hope something in here is helpful...