Another way is through reduction of your permanent BP or EP to zero. The HP and MP may be bought back after you have lost them, so take care that you do so whenever possible. If all participants are willing, the arena allows you to fight to the permanent death as well. If your character is risking permanent death in some other way, it will be clearly indicated. The prices for some items depend on the season and their availability.
Some items are more expensive in the summer, while others peak in the winter, fall or spring.
Other changes in price can be caused by raising or lowering your reputation, changes in your bargaining skill and raising your Intelligence skill. Some monsters are vulnerable to some types of damage, just as some are resistant to some types of damage. Skeletons are a good example of this, as their brittle bones can be weak to bashing damage. However, they are resistant to arrows, since there isn't much for an arrow to stick into. Use your sense when you come up against a monster that seems to be resistant to a certain type of damage.