What is the opposite of fad?

As the other answers suggest there are several ways of saying what you want to say, but in the context of the sentence that you provided, I would suggest "here to stay."

"Are fidget spinners just a fad, or here to stay."

If something is here to stay, it has stopped being unusual and has become generally used or accepted:
Blogging is here to stay.

Reference: Cambridge Dictionary

Sometimes a classic is the opposite of a fad or fashion:

This plain black cardigan is a classic piece that will be useful in your wardrobe for years.

From m-w.com

Definition of classic 1 a : serving as a standard of excellence : of recognized value classic literary works a classic case study on hysteria b : traditional, enduring classic designs c : characterized by simple tailored lines in fashion year after year a classic suit

You might consider staple

4. A basic or essential supply.

   Rice is a staple in the diet of many cultures.

5. A recurring topic or character (in creative works).

or perennial.

3. Continuing without cessation or intermission; perpetual; permanent; unceasing; never failing.
4. (figuratively) Enduring; lasting; timeless.

Often, the opposite of a fad is described as a classic (or, in its adjective form, a classic [whatever]). This usage is especially common in fashion, but I think can be applied in other industries. The general definition, from Oxford Dictionaries:

ADJECTIVE

1. Judged over a period of time to be of the highest quality and outstanding of its kind.

   1.1. (of a garment or design) of a simple, elegant style not greatly subject to changes in fashion.

NOUN

1. A work of art of recognized and established value.

   1.1 A garment of a simple, elegant, and long-lasting style.

And some further explanation of the fad-trend-classic gamut, from the world of fashion (in this case, jewelry, but very similar discussions are found in other sub-genres of fashion; all bolding added):

Typically, fads last for a total of one season, but they can also last less than a month.
. . .
Trends have a much longer lifespan than fads. . . . The primary difference between a trend and a fad is that trends have the potential to be long-term influencers on the market.
. . .
Classics are forever.

"Fad, Trend, or Classic: What's the Difference?", MarkSchneiderDesign.com, 2014

While you will (most?) often see these distinctions discussed in the realm of apparel, they are also very often used in other areas.

Some relevant examples:

• Before you get your child the latest fad toy, consider these top 12 classic toys that have been around since your childhood and have lasting appeal.
  "12 Classic Toys That Still Rock", FamilyEducation.com

• "Forget The Fads, Stick To Classic Toys", National Public Radio, Dec. 20 2011

• "Fad or classic? A tale of two games", Seth Owen, BoardGameGeek.com, Sep. 30, 2015

Note that it's really hard to judge something a "classic" before at least some time has passed, even if we think it is headed in that direction. So if you are wondering whether fidget spinners are going to be here-and-gone or will be around for a very long time, you could say:

Are fidget spinners just a fad or are they destined to be a classic (toy)?

A slightly more concise way to say this would be to use the term "new classic", a slightly-oxymoronic phrase meant to suggest that some new thing has all the hallmarks of a classic. So:

Are fidget spinners just a fad, or are they a new classic?

I note that another answer suggesting "classic" has been posted while I've been writing this; I'm going to go ahead and post it anyway for its examples, and also upvote that answer.