How would an animal ever accumulate enough merit to warrant rebirth as a human? i have only a basic knowledge of Buddhist thought but have hit a problem that i have not been able to locate an answer to. so any pointers would be appreciated...

everything i read suggests that to be born as a human being is very propitious as it allows the degree of reflection/mindfulness required to be able to understand the teachings and make progression towards enlightenment.

but if these fortunate circumstances are wasted and actions in your current life result in rebirth in a lower form, there seems no way that i can see to progress even to another human birth, let alone anything else, if progress is predicated on awareness/mindfulness/ability to understand the teachings etc

how would something such as, for example, a dog ever be able to accumulate enough merit to warrant rebirth as a human? i have a dog and all he wants is food and walks, he never seems that reflective.

seems like a game of snakes and ladders in which - other than when playing as a human - its going to be all snakes.

thanks for reading.
In the Jataka tales (Similar to Aseop's Fables ) there are many stories about the Buddha's various past lives. These are tales for children and normally come with a moral. 

There are a ton of them, and they normally end with the animal the Buddha is reborn as helping out in someway that is aligned with the teachings. 

You can see a few of them summarized quickly without the entire back plot of a fable here.

It is absolutely correct that in the Buddhist worldview a human rebirth is of great advantage. Animal existence is not what most of us would consider fun. As one teacher once reminded me, you might be a pet, or you might be reborn a deer in a forest of wolves. An animal life is mainly fear and instinct. The characteristic of their realm is that of Ignorance. 

As you yourself pointed out, your dog (Who is lucky and has food, shelter, and someone looking out for them) is not often reflective. 

Anger the characteristic of the hell realms is more damaging, and can lead to a large snake on the game of chutes and ladders. 

Your dog though, in your ownership, is likely not accumulating massive amounts of negative karma. 

I hope this helped to answer your question.