Just to be clear on this:
To save, press [the button you have mapped to] Start and [the button you have mapped to] B.
To resume your saved game, start up the game and use the in-game menu to select your file.
Do not at any time touch PJ64's System->Save/Save As/Restore/Load functions.
If you're following the correct procedure and are still having difficulties with saves not saving, there may be a problem with the permissions on your save folder. (Most likely you are using Windows Vista or 7?) Probably the simplest way to get around this is to run PJ64 as an administrator when saving your game (all the time, basically). Otherwise, you'll need to alter the permissions on PJ64's save folder to allow your user account to write to it, or change the save folder to one that your user can modify.