Now for Day 3 and another excellent question...
First let me define what 'staying power' means to me.
It's meaning, as I see it, is actually two-fold:
First it means that the game lasts the test of time. It remains popular over the years, sometimes even beyond it's own publishing life. There are many gamers out there (myself included) who regularly play older editions of RPGs still in production, as well as ones long since out of print.
A second possible meaning is that it remains popular at my table. My players and I return to that particular game again and again. This angle is especially important, interesting, and impressive to me, as I get enjoyment out of trying out new games. If in the course of doing so I return to one particular game on a regular basis between my taste testing of others it means that the RPG in question is something special and rather extraordinary.
Now that we've established what staying power means, what gives a game this much coveted quality?
In the grand scheme of things, that is to say the 'big picture' of the RPG hobby as a whole, I have no idea. Seriously. The perfect example is Dungeons and Dragons. Why does it have such staying power? No clue really. It was first, it was marketed better than others (few RPGs are marketed at all outside of a game community that already knows about them), and it definitely functions as a game that can be played for an extended period of time (I'll get to that more in a moment). But with so many other games with more logical, simpler, more unified mechanics, why does it remain on top? I really couldn't say.
For me personally, a game has staying power if it...
Effectively emulates the feel and function of the genre or setting it covers.
If you are creating a Star Trek game and it things within work the way Star Trek works, that game will last as a go to system for running Star Trek. A Fantasy game wherein the magic system makes magic feel powerful, mysterious, and dangerous if not handled correctly is a game I will go back to when I want to run Fantasy.
What? It happens.
Enables gradual/tempered build up of skills and abilities over time.
As much as I play RPGs for the story, character development, world building and mystery solving, they are still, in the end, games.
There needs to be a system for expanding upon and improving your character. Said system can't see the characters improve too quickly, as that means the player will reach the end of their desire to play the character sooner rather than later. That's a staying power no-no. Alternatively, they will want to play their god-like, ultimate, ultra-character and the GM will get bored trying to come up with yet another reality shattering challenge week after week.
Don't get me wrong, I love reality shattering challenges, but every week? Enough is enough.
Characters that improve too slowly, while less common, can also be a source of frustration and the game that features such a slog to advance may also not be one the group wants to return to.
A final note: Games where you don't improve at all get really old really quickly. The GM can't increase the threat or expand the scope of the game, and after a while it tends to feel tedious.
Has enough options or a system for easily generating new material so that each play through feels different enough from the previous one.
If I am playing a Mon Calamari Starfighter Pilot this campaign, I will probably want to play a very different character in the next one. If I can't, or if the first character and the second feel too similar, I will probably not want to play again.
When gamers get a new game, the first thing many of us tend to do is make a character. I know a lot of fellow RPG fans who make a few characters. I tend to make up two or three of the same character.
What? Like, you make up three Dwarven Clerics? Yes. That it exactly what I do. Why? Because I want to know if a game can handle two or three of the same or similar PCs in a single session or even a campaign. I recall making three Elven Wizard for D&D 4E and being very disappointed with the lack of options. Two out of the three were so similar I lost interest almost immediately.
You want a game that you can play, play again, and play again and again and each time it feels a little unique or you discover something new about it. A campaign that can use the same rules, rules that uphold the genre, yet let you do and say something different each time you haul it off the shelves.
That's staying power my friends.
The following games are ones that I find to have a lot of staying power.
Each one is a game I have run multiple campaigns with and I find myself returning to time and again. There are others, but these stand out as being notably replay-able and unforgettable.
Ars Magica 3rd Edition (White Wolf Publishing)
Champions 4th Edition (ICE/Hero Games)
Mekton, 1st and Mekton II, 2nd Edition (R. Talsorian Games)
Star Trek, The Role Playing Game (FASA)
Star Trek, RPG, Various versions (TOS, TNG, DS9) (Last Unicorn Games)
Star Wars, The Role Playing Game (West End Games)
Traveller, 1st Edition and MegaTraveller (Game Designers' Workshop)
Which ones have staying power for you?