Expected Results::
Every hour, unless a pet has a stimpack in use or has full energy already, your pet is meant to gain 1 energy. On the energy bar on the pet's profile page is a (+1 on -insert time-) indicating when this energy increase will occur.

Observed Results::
I've noticed a few minute delay on the energy gain in the past with my pets. The most recent case of this has been with Zohar, and he is the pet I'm using in this bug report as an example.

While having 4 energy, Zohar was supposed to gain +1 at 00:03, as shown here. However, as you can see, at 00:11 he had yet to get this energy and the (+1 on -insert time-) was still saying 00:03. The energy wasn't gained until 00:12. Be it a coincidence or not, I find it worth mentioning, is that my other Symurgh, Areli, was meant to gain energy at 00:12 and both of them received the +1 at this time. They're twin brothers if that has any correlation to this incident.

Related Question::
While I'm posting an energy related bug I may as well ask a question I've had for a while now. Why does exploring reset the 1 hour energy gain? If you go to an island with only a couple minutes to go for the +1 the hour countdown starts over and the energy you were about to gain is not received. If you explore, leave the page, and return a few minutes later to finish your exploring on that island it resets again.

1) This happens due to a midnight reset and also may happen once every 4 hours when new cycle starts. Earlier we had a 30 minutes maintenance mode every night but now the script is optimized to let the players continue playing while it is processing all routine tasks and starting new day (this includes daily backup, processing pet food and daily income, inn guests, generating new quests etc.). This script is called cron. It's the same process that handles pet energy, statuses, number of available islands etc. Today it started processing new day at 0:00 and finished at 0:11, so it was able to recalculate pet energy at 0:12.

2) It works like this with any pet activity and was coded this way with purpose. A pet should have a full hour of rest to regain energy. If we wake up a man at 3AM, force him to run 3 miles and let him sleep further, he won't wake up rested at the morning (and we will hear everything that he thinks about us). The same thing happens with pets.

^LOL, Angel, that explanation though XD