I hate to say it but if your boss doesn't know about your work "expenses" are you getting reimbursed for it?
Also, if you keep hitting the limits(depending on how high the limits are) on your personal credit cards, it will definitely reflect on your poor spending habits to your boss. I would ask him about the company card and tell him the reason you keep hitting your limit, is because you're incurring too many work expenses. I would think he would understand unless he is reimbursing you. If he is, then your plea may fall on deaf ears