Chazal (Misechta Sofrim 2:1) state, להדליק אסור ישן בנר, "It is forbidden to light [Chanukah lecht] in an old lamp." The Bnei Yissaschar (Kislev 4:9) explains that a חרס כלי, clay lamp, can never be cleaned. After you use it once, it appears disgusting (see Mishnayos Shabbos 2:4). Therefore, it is a ביזוי מצוה, a disgrace for the mitzvah, and it shouldn't be used for Chanukah lecht.
But this can't be the only reason for the prohibition. If it were the only reason, it would be forbidden to use clay menoros on Shabbos and yom tov, as well, and not only on Chanukah. There needs to be an additional reason why we don't light with a ישן נר, "old lamp" on Chanukah.
The Bnei Yissaschar says that we can't light in a ישן נר, an old lamp, because we must remember that Hashem performs Chanukah miracles for us every year. We aren't only commemorating a miracle that happened in ancient times, millenniums ago. The miracles return each year.
About Purim, Chazal (Megillah 17.) say, יצא לא למפרע מגילה הקורא. The Bnei Yissaschar repeats from his Rebbes, למפרע מגילה הקורא, if one reads the megillah like it was an episode that happened in the past, יצא לא, he didn't perform the mitzvah correctly. Every generation has its Haman (or Hamans) who want to wipe us off the map of the earth, and Hashem saves us each year anew, in the merit of the mitzvah of reading Megilas Esther. We aren't solely commemorating the past; we celebrate the salvations that Hashem grants us each year.
The Bnei Yissaschar says that something similar occurs with the Chanukah lecht. We aren't only commemorating a miracle of the past. When we light Chanukah lecht, the miracles recur again. Thus, Chazal say, אסור ישן בנר להדליק, "It is forbidden to light in an old lamp." When we light the Chanukah lamps, miracles occur in our time again. It isn't an "old lamp". It is a salvation that is happening to us today.
One hundred years ago, in the year 5683, someone came to Reb Itzikel of Antwerp zt'l and told him that he must travel immediately. However, he did not have a passport, and ordering one would take too long. In response, Rebbe Itzikel gave him a bencher and said, "If you need a passport, take this." The man showed the border police his "passport." The policeman skimmed through the pages and stamped permission for entry next to the words הניסים על. (A picture of the passport can be found on the last page of the booklet) This miracle didn't happen on Chanukah, but the origin of the miracle came from Chanukah. It is an example of the miracles that recur each year.
