We can look at history for the answer to your question. Some franchises have been running for decades and remain extremely strong today - Call of Duty, FIFA, Madden, the Sims, and Grand Theft Auto all span decades, lots of installments, and multiple millions of players. Some franchises have been relegated to specific niches - no longer the headliners they once were but still remain reliable, like Mega Man, Street Fighter, Battlefield, Civilization, and Just Dance. And finally, we must consider the franchises that have essentially been relegated to the dust bin of history. They’ve had their day in the sun, but a new game announcement in the series won’t really generate a significant amount of interest - Tony Hawk, Guitar Hero, Turok, Castlevania, SSX, Medal of Honor, Prince of Persia, Wing Commander, Ultima, Unreal Tournament, Command and Conquer, and Twisted Metal.
If you consider the context, it should be clear that franchise games that are able to find an audience consistently, even if that audience isn’t massive in size, can carve out a sustainable niche for themselves. The dead franchises are those that were unable to find sustainability with their audiences and generally fielded more than one failed game. In each of those cases, the publishers looked at the total costs they thought would be necessary to create a game within that respective franchise and compared that to the expected return on that game and decided it wasn’t worth the risk.
That said, hope springs eternal. A lot of publishers will leave a franchise fallow for a long time. The longer a franchise is dormant, the lower the bar for a revival success. As we’ve seen with the revival of formerly-dormant IPs like Crash Bandicoot and Killer Instinct, fans can always hope that maybe someday Golden Sun will rise again.
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