I LOL'd at the comment directed at Cin. You know, some of us are actually just as capable as Cin about answering your questiions.
However, the yellow bar in question is your pet's hunger bar - not your pet's... tiredness bar.
Yes, it is filled all the way back up once it Levels, but if you go to the Stables, you'll see these potions called Pet HGP potions, or something of the sort. They're yellow, I believe. Not on SRO or anything, so I can't check for myself. Those will restore your Pet's; hunger to keep it from dying.
Note that the higher your Level, the longer it'll take for you to level up, and the more and more you'll be needing those potions, unless you want your pet to die. (Animal abuse!) But usually, you won't really, REALLY start needing those potions until around 3X, I'd say.
Just feed your Pet. Your wolf gets hungry, too.
