@inferio,
The problem here is that "No matter what" is an English idiom. If you
translate it word for word into Latin, it makes no sense. So you have the
option of expanding it into something like "Nothing that happens
prevents life from going on" or using an equivalent such as "Whatever
happens, life goes on." I think the second is the better choice and I like
the translation Bitmap gave you on latindiscussion.com,
quidquid accidit, vita pergit.