Here is the text for "'Push' an Animal" for the Handle Animal skill:
To push an animal means to get it to perform a task or trick that it doesn’t know but is physically capable of performing. This category also covers making an animal perform a forced march or forcing it to hustle for more than 1 hour between sleep cycles. If the animal is wounded or has taken any nonlethal damage or ability score damage, the DC increases by 2. If your check succeeds, the animal performs the task or trick on its next action.
If the action of the trick takes longer than its next action, what happens?
For example, skills like "Bury", "Heel", "Sneak", etc. could all take longer than one round. Bury is the most obvious. It includes the animal finding a hidden spot and then burying an item. This implies multiple minutes of actions, not just one action. But, I cannot see a situation where you would want an animal to heel for six seconds and then stop or sneak for six seconds and then start making lots of noise.
For "Attack", we know from the "Down" trick that:
An animal that doesn’t know this trick continues to fight until it must flee (due to injury, a fear effect, or the like) or its opponent is defeated.
So, pushing an animal to attack clearly allows it to continue longer than one round. Does the absence of similar text imply that the other tricks I mentioned are performed for a single action, and then the next round, the animal must be pushed again to do the same trick?