No. The basic service is free and it never expires.
However, there are quite some restrictions to free service users (incl. Free & True Users). They can only create two automatic backup tasks; can have only 2 FTP connections; can synchronize folders from local PC to online storage, but cannot synchronize from the other direction, etc. In addition, free service users don't get the same level of customer support than premium users.
For more detailed information, please visit www.drivehq.com, click on Premium Service.