Starting October 6, new legislation came into force for minors accompanied by a parent or an adult person, according to Law. 169/2016 published in Monitorul Oficial. Thus, the parent statement of agreement is valid for several trips and it is no longer required to declare the purpose and travel route.
The new law provides that: "[T]he minor who is the holder of a travel document individually or, where appropriate, an identity card / electronic ID cards and travel abroad with one parent be allowed to leave under the same conditions and along with it only if the parent accompanying a declaration of the other parent showing consent on making travel abroad for a period not exceeding 3 years from the date of completion or, where appropriate, evidence death of the other parent. "
The Law can be found here: http://www.cdep.ro/pls/proiecte/docs/2016/pr185_16.pdf