What happens at the end of an Assured Shorthold Tenancy Agreement?

Campaigning and Policy

I signed a 12-month Assured Shorthold Tenancy Agreement with my tenant which is due end soon. I am happy with the tenant and she wants to stay. I was under the impression that the tenancy agreement would just continue on a rolling month-by-month basis, but can't find any reference to this in the agreement or on the web. The letting agent is pushing me to sign another 12-month agreement - but can't tell me what the benefits of a new agreement are. I suspect they just want to charge me another letting fee.