Both Amaterasu and Chibiterasu can increase their overall Solar energy through a variety of means. Primarily, the two increase their health through the collection and use of Praise. The secondary means of increasing overall Solar energy is through the accumulation of Sun Fragments. Via these means, Amaterasu can get up to 20 units of Solar energy by the end of a playthrough, whereas Chibiterasu can only rack up 10 units.
Because Solar energy is a unit of health, it only makes sense that it can be both lost and gained back again through various means. Typically, Amaterasu and Chibiterasu can lose health on while engaging in battles that take place in the rings created by a Demon scroll or through attacks during a boss battle. Both can also lose health due to elemental attacks outside of battle, such as burns, poisonings, or drowning. However, they do not tend to lose too much health, and both games provide a number of different ways for each to heal.
The use of Holy Bones is the most prominent method for healing either divine wolf. Defeated enemies also occasionally drop Spirit Globes that can restore varying levels of health. Equipping a Holy Artifact such as the Wood Mat is a good method for restoring health when a Merchant is nowhere to be found, typically in dungeons or a Devil gate trial cave or during boss battles, if possible. This is done at the expense of some Yen, but nearly all money spent can immediately earned back by engaging in a battle or race of some form. The same can be accomplished for Chibiterasu through the use of the Scent Charm, which heals him while he is fighting.
In the case that either runs out of health, they are faced with a death screen during which, if an Astral Pouch has been sufficiently filled, they can be revived. Otherwise, their bodies are rendered useless and scattered to pieces. However, equipping the String of Beads for either wolf will prevent their death in battle, in addition to removing the need to accumulate health altogether.