The Terminator franchise has been not to great and the reason is well, the story itself. Let me explain:

-Skynet is an AI that becomes self aware Aug 29. 1997 and the world gets nuked (Judgment Day), leading to a war with Skynet against The Resistance.

- John Connor, the leader of the resistance, sends back Kyle Reese to protect John's mother, Sarah Connor, from being killed by a Terminator. If the Terminator succeeds, he kills John Connor, and John Connor would not lead the resistance to victory.

- Kyle Reese and Sarah Connor conceive the child that would be John Connor.

- Kyle Reese dies and the Terminator gets crushed in a Cyberdine factory.

- Cyberdine now has future technology that they are trying to test and gain information that would bring about the creation of Skynet.

- Another Terminator (T-1000) is sent back in time to kill John himself. Another attempt to take out John Connor. But John from the future reprograms a T-800 to take out the T-1000.

- John Connor and T-800 bust out Sarah Connor from a mental hospital, where the T-800 gives information on Miles Dyson, who's work would help create Skynet.

- Sarah Connor goes on a solo mission to kill Miles Dyson, and ultimately can't kill him. The T-800 and John Connor go to Miles Dyson's house, to find Sarah and the T-800 explains everything to Miles Dyson.

- The team plans to destroy all of Miles work, and blowing up Cyberdine itself. It leads to a successful attempt, at the sacrifice of Dyson himself. The terminators and the remnants of the first terminator that tried to kill Sarah, were destroyed after a final battle between the T-100 and T-800 with the help of Sarah.

- Now that Cyberdine is destroyed and no evidence is left behind, they stopped the creation of Skynet and Judgment Day from ever happening.

This is the paradoxical problem of the terminator franchise. If John didn't send back Kyle, he wouldn't have been born. If Skynet didn't send back the first T-800 it would have never been born either. Not only that but because Skynet sent a T-1000 to kill John, and future John sent a T-800 that told Sarah and Miles about what would come, they stopped it Judgement Day. Therefor if Skynet didn't send a T-1000 back, John Connor wouldn't have sent a T-800 back, and that would have allowed Judgement Day to happen. But Judgement Day was prevented. Therefore making John Connor insignificant.

This is why the Terminator franchise has failed. It ended with T2. It's a self contained story. Despite attempts like T3, where Judgement Day was only postponed, Salvation (which showed a future war that was not the one fans wanted to see), Genisys with an altering of the timeline of the altering of a timeline (I'll explain in bit), and Dark Fate, who kills John off because his Judgement Day never happened, yet a different judgement day occurs (which makes T1 and T2 pointless). You cannot have a great Terminator film without it being coherent with the first 2 films. I personally think T3, despite it's flaws, was the sequel that made the most cohesive sense.

But the Terminator started as a sci-fi horror film, that went sci-fi action since T2, and has been about action since. I feel like the Terminator franchise has lost it's ways and because T2 was a great action film and technologically advanced , the sequels needed to be action and technologically advanced as well. The action wasn't what made Terminator 2 successful, nor the CGI, although it did help because it was groundbreaking stuff. But it was the story, and the characters drama that made it so good and connectable to audiences. Today with a plethora of CGI films, if The Terminator is going to be just that, then there is nothing special about it. If the story is not cohesive to what is established, then fans won't care.

I think that in order to make another terminator film series that works, you would have to go back to the beginning and start at the original timeline and just have that unfold. The original timeline being Sarah and some other man other than Kyle, having John Connor, and Cyberdine creates Skynet without the data of the first T-800, Skynet becomes aware and John survives Judgement Day and leads the resistance to victory, and then maybe end the film series where the T-800 and Kyle go back in time, where it creates the time paradox presented in T1. John in the original timeline, not aware that Kyle would be his father if he sent him back in time, and he viewed Kyle as his trusted ally to do the job correctly.

The first film would have to be a drama, dealing with the concept of Skynet and what it is supposed to be, and if there are limitations to what Skynet should or shouldn't do. Sarah raising John in 90s LA with the riots. At the end Skynet would become aware, and Judgement Day would happen. The second being to more of back as a sci-fi horror, with the terminators hunting down remaining humans, and John starting to take command, leading into the third movie with a huge battle and the future war we've always wanted to see, ending with the time paradox mentioned in the paragraph above. To tell one long, cohesive narrative that will tie into T1 is how I feel the movies should be done, if they were to try to revive the franchise back from the dead a third time.