It sounds like the tenant vacated without notice. If that is the case, then you do not necessarily need to refund any rent to the tenant.
On a month-to-month rental agreement, as a landlord you are entitled to a 30-day written tenancy termination notice from the tenant before she is released from rent payments. (ORS 90.427 (3)(a); ORS 90.220 (8)(f).) Assuming the tenant did not give you a 30-day notice, you are entitled to rent for 30 days after the vacate date. This means that you can keep any rent that she has already paid, plus take any remaining rent due for that 30-day period out of the security deposit (if you have one).
There is one caveat, however. You do have an obligation to make reasonable efforts to re-rent the RV space. (ORS 90.220 (8)(d); ORS 90.410 (3).) If you are able to re-rent it, then the old tenancy terminates as of the date the new tenancy begins and you would be liable for returning the rent to the old tenant from that date forward. (Note: You are not necessarily obligated to steer new tenants to the old tenant's vacant space. The reasonable practice would be to let any new tenants choose which vacant space they want on their own.)
The bottom line is that without a 30-day written vacate notice from the tenant, you can keep the rent until the space is re-rented to a new tenant. You are then obligated to refund the remaining withheld rent to the previous tenant. However, as usual, consult a knowledgeable attorney if any complications arise.
(FYI: If you happen to have any written, week-to-week tenancy agreements, the same rules apply except that the 30-day notice period becomes a 10-day notice period.)