@Carrie Pledger
In your state it is clearly legal to access a tenant's premises for non-emergency reasons with 24hrs notice, as provided by the Landlord-Tenant Code of Virginia. Here is a copy of the law (as if you needed any further proof!):
§ 55-248.18. Access; consent; correction of nonemergency conditions; relocation of tenant.
A. The tenant shall not unreasonably withhold consent to the landlord to enter into the dwelling unit in order to inspect the premises, make necessary or agreed repairs, decorations, alterations or improvements, supply necessary or agreed services or exhibit the dwelling unit to prospective or actual purchasers, mortgagees, tenants, workmen or contractors. The landlord may enter the dwelling unit without consent of the tenant in case of emergency. The landlord shall not abuse the right of access or use it to harass the tenant. Except in case of emergency or if it is impractical to do so, the landlord shall give the tenant notice of his intent to enter and may enter only at reasonable times. Unless impractical to do so, the landlord shall give the tenant at least 24-hours' notice of routine maintenance to be performed that has not been requested by the tenant. If the tenant makes a request for maintenance, the landlord is not required to provide notice to the tenant.
I don't believe the tenant is doing anything illegal, but rather just do not want you in what they view as their home.
Good luck!