Linda Hamilton opted of Terminator 3: Rise Of The Machines since Sarah's proposed storyline would have just been recycling the events of part two. The character was greatly missed from parts three and four, and it was generally felt that Salvation suffered from the lack of Sarah (though Hamilton did cameo via recorded tapes) and Arnies Terminator.
This should explain the fan fiction plotline of Terminator: Genisys, which reboots the timeline and bands together Sarah, Kyle Reese and The Terminator for a new adventure. It even throws in the T-1000 and Miles Dyson for free, but none of this prevented Genisys being considered the worst film in the series.
The plot is a convoluted mess, the action is substandard and the performances suck, so not even the intense fan baiting of bringing back iconic characters could save it. It remains to be seen where the series will go from here, but a direct Genisys sequel seems very unlikely.
Handsome. Charismatic. Intelligent. Noble. Witty. I'm none of these things, but I'm a half decent writer, I guess.