In theater, "strike" refers to removing something from the stage; more specifically, tearing apart the set.
The strike has to take place after the final performance so as to store all the props and furniture used in the play and to clear the space for the theater's next show.
The speaker considers his love to be his muse. The speaker wants his muse to help him immortalize his love. The speaker fears that his love is growing old faster than he would like.
