I noticed that things that change the energy level of a pet will reset the countdown back to one hour, even if the pet didn't have full energy before decreasing it, or if its energy didn't fill up all the way after increasing it.

Examples:

My pet has 9 energy, and it's supposed to regain 1 energy in 5 minutes. I explore an island. As soom as  I go in, my pet goes down to 4 energy, this is normal, but its energy +1 counter goes back up to one hour.

My pet then finds an oasis and drinks from it, recovering 5 energy, but its energy +1 counter goes back up to one hour.

This is not a bug but rather a mechanics that needs a clarification. Pets need uniterrupted rest to regain energy. The minimum time of rest is one hour, which restores 1 energy point. If a pet is asked to do anything within this hour then the counter resets.