OK... You're right. Nights indeed crashes after you finish a stage but this happens *sometimes* for *some people*.
I encountered the same problem only today and after reading some stuff on the SSF site (using Google's translation) I understood that this random crash happens because of some changes and will be fixed in the future. However, if you keep playing the same stage over and over you'll manage to avoid the error and continue.
You'll notice that this version of SSF has some more options than the previous. You *might* be able to fix the problem by selecting one or more of the new options. Also from the settings of the emulator try setting the frequency amount of the secondary SH2 to 100 (it's on 75 by default).
Important note: You have to delete the settings and Backup RAM files of the emulator
EVERY time you download a new version of the emulator (better to delete all the directory of the emulator and keep only the BIOS file). Using files that were used by older versions of the emulator with new versions can result in serious problems (some games won't work correctly or even not at all).