Can you provide some more information? A link to your site, the permalink option currently selected, what type of operating system and web server your site uses, WordPress version, etc...
Without any details, here are the recommended troubleshooting steps:
Visiting the permalink settings page flushes the rewrite rules. It is possible that your theme or a plugin is doing something funky with the rewrite rules, or it could be that you have selected a permalink structure that isn't supported by your system.
The first thing you should try is setting your permalink structure to the default (first option). If this fixes the issue, then your system is probably not setup to properly support permalinks.
The next thing is to try disabling all other plugins (besides the Promotion Slider), visit the permalink page and then try loading up a page or promotion. If it works, then you know the issue was with another plugin... you just won't know which one until you reactivate one at a time, revisiting the permalink page each time and testing your pages.
If that doesn't work, then disable all your plugins (except the Promotion Slider) and switch to one of the default WordPress themes, visit the permalinks page and then test your pages. If that works, then it is an issue in your theme.
If all else fails, then it is likely a bug in the Promotion Slider code... however, since thousands of people use it and haven't reported this issue, then I am fairly certain that one of the above troubleshooting steps will reveal the source of the issue.