The discovery of frequent sequences in temporal databases is an important data mining problem. Most current work assumes that the database is static, and a database update requires rediscovering all the patterns by scanning the entire old and new database. In this paper, we propose novel techniques for maintaining sequences in the presence of a) database updates, and b) user interaction (e.g. modifying mining parameters). This is a very challenging task, since such updates can invalidate existing sequences or introduce new ones. In both the above scenarios, we avoid re-executing the algorithm on the entire dataset, thereby reducing execution time. Experimental results confirm that our approach results in execution time improvements of up to several orders of magnitude in practice.