To answer to your question,what kills good franchises is that their development studios stop being independent and being bought by big publishers.
When a big publisher buys an independent developer studio,expect the game series this studio was making to at least change in the best scenario,or totally die in the worst case scenario.
Konami bought Hudson Soft at a time where they had 2 games in the making,preparing them to be 3DS launch titles,and one of them was a Bomberman game. From the moment Konami bought that studio,they forced it to stop the work in the games they where making,and start making a Facebook game. After 6 months when the Facebook game was finished,Konami fired all employees of Hudson Soft and practically killed the Bomberman franchise.
EA bought Bioware,and as a result we had Dragon Age 2 which was the worst game of the series,and the transformation of Mass Effect from an RPG to a cover based shooter. They bought Crysis and transformed its single player to a shallow linear game,and its multiplayer to be more like Call of Duty,and thus uninteresting. They bought Maxis and they turned Sim City to a shorter game with always online DRM that kills any interest players might had for the game. They bought DICE,and they turned Battlefield from a strategic based war simulator to a more arcade-y and game-y game that isn't realistic at all,and doesn't require strategy,in hopes of stealing fans from Call of Duty.
Microsoft bought Rare,and Perfect Dark turned from a revolutionary shooter franchise to an over-simplified mediocre piece of poo,and then they decided that Rare should only make Kinect games. Conker and Perfect Dark franchises died.
As you can see,when a developer studio gets bought by a publisher,it is almost 100% certain that the main focus and gameplay of a series will change,and most times this change ends up being negative.
On the other hand,independent studios show that as time passes their game series becomes better instead of worse.
Witcher 2 fixed lots of mistakes from Witcher 1,and most initial mistakes of Witcher 2 got fixed by patches,while developers acknowledged the problems of Witcher 2 and promised to fix them for Witcher 3.
Mojang is keep making changes to Minecraft that makes it a better game instead of worse.
Croteam made Serious Sam 3,a really good game for the series that stays true to the gameplay formula of the series while feeling fresh with all the new graphics,music and things that while making the formula feel fresher,doesn't completely change it,doesn't change the core elements of the gameplay the series is known for.
It seems that developers that keep themselves independent tend to produce better games than those who sale themselves to big publishers.
Now I'd really like to see something: Could someone write a list of all the game series that died in recent time,like the last 2-3 years ? It would be pretty interesting I think.