Connotations of "all the rage"

Per your definition, it is popular or fashionable at the moment. How long this “moment” will last is hazy — if you are talking about web design styles, the usual answer is a couple of years, and so is worth noting for a site build. If you are talking about a TV series or toy, it is liable to be six months or until Christmas.

There is an implication that something is popular within a particular culture — that may be popular culture, Sloane culture, or Azerbijan culture. So it might be “all the rage in Blackburn” or “all the rage amongst young Trekkies”. It is often used for something that defines a particular culture or subculture for a while.

It can carry an implication that if you get in now and exploit it, you can make some serious money. But do not commit long term, because however popular it currently is and however much you extend the usage of this fashion, it will not stay popular longer term.

Yes, that's about right. However, in my opinion, the ephemeral aspect of this idiom has grown over time due to its association with other components. I've outlined a few here:

The hula hoop was all the rage in 1959.

Wearing bright yellow trousers was all the rage back in the day.

Using the word frack instead of f#$k is all the rage at the moment.

Wearing a moustache is all the rage nowadays.

In other words, this phrase is inevitably associated with a component of time which implies something transitory.

Collins gives, as one meaning of the word "rage":

a fashion or craze (esp in the phrase all the rage) (link)

The term "craze" is of note, as "rage" has its origin in the word "rabies" (see the Online Etymology Dictionary).

"Rage", in every sense, connotes an intense and transient state. So it's safe to say that the popularity of something that's "all the rage" is bound to fade.