(1) Every band has a shelf life; BB had expired.
(2) BB finally expired because every band has a shelf life.
I don't think the connection gets stronger or is weakened, but the word because establishes a causal link (that is, it provides a reason that something happened).
The first version makes it seem like the demise of BB was inevitable; it was only a matter of time. The second version is attempting to explain why BB broke up.
SO, are you trying to assign a cause, or are you merely reflecting on a reality in a philosophical way?
Also, this construct gets tricky when the cause isn't true and accurate. Consider:
Everyone must die eventually; my grandfather passed in 1986.
My grandfather passed in 1986 because no one can live forever.
That second sentence sounds awkward, because mortality wasn't the cause of his death. It's not ungrammatical, but it's not very sensible, either. It would be better to say something like:
My grandfather passed in 1986 because he had a heart attack.
We can get around this by using a semi-colon:
My grandfather passed in 1986; no one can live forever.
In short, we are trying to associate a general truth with a specific instance. Of the two versions you've given, the first works well, and the second doesn't. BB didn't expire because every band has a shelf life; their "expiration" merely reinforced the notion that every band does have a shelf life (with the Rolling Stones being one notable exception).