Is the priority order sequential as you show in your post or is the left pane sorted by mod name descending? If priority order appears to be in random order, this is because the grid is sorted by something other than the priority. If you look at the top of the left pane you'll see the title row for the grid that has Mod Name, Flags, Category, Nexus ID, Version, and Priority. It may not be exactly this since some columns can be hidden. In any case, the import part is determine which of the column titles has a small up or down triangle to the right of the title. If you click Mod Name for example, the left pane sorts by the Mod Name ascending. Click Mod Name again and the sort changes to Mod Name descending. Click Priority until the numbers are sequential from 0 to n.
If the priority order is in sequential order, you might verify you are in the right profile first. I sometimes make this mistake when checking something in another profile and forget to switch back before closing Mod Organizer.
If this isn't it, you can drag them back into the correct order. You might do this for just the vanilla plugins and the DLCs, then restart Mod Organizer to verify the order sticks after Mod Organizer restarts. If the order doesn't stick after restarting Mod Organizer, you might have permissions issues or perhaps wonky antivirus software interfering with Mod Organizer for some reason.