No, renewal of F2, a dependent visa for F1 is not required to renew as long as F1 still holds the valid status. Status is considered valid while the person is taking full time courses and also is valid when the person goes on OPT to seek for an active employment after graduation. If the person is unable to find a job within the period of OPT, then he/she must leave the country within 60 days after its expire to be considered in status. Hope this helps.