My favorites are Suikoden, Grandia, (Xeno)gears and Chrono series.
Sadly most of them, if not all are falling into obscurity.
Suikoden
The Suikoden series got its team disbanded and the only Suikodens that came out since were outsourced and didnt share the same overworld the series is known for. Suikoden V was praised by the press, but it didnt stop Konami from disbanding the team and beeing unable to bring it back up to the new generation of hardware.
I know that Konami tried to rehire the series creator since but he refused to return to Konami.
Status: Dormant.
Possibility of return: Unlikely
Grandia
Grandia has a troubled history. While the games have been consistently good, despite a dungeon crawler entry that was unwanted but was decent and a Grandia 3 that was a good game but couldnt compete with its predecessors.
The main problem is the founders of Game Arts and creators of the series have died or left the company.
The only sign of life from the Grandia series was the PSN re-release of the first game. But, the developer still exists, even if bought by Gungho, and i'm sure there are still Grandia fans inside the company.
Status: semi-dormant
Possibility of a return: Possible, though most likely on portale formats.
Xeno(gears)
This one is a rollercoaster. Xenogears itself was supposed to be 7 episodes with Xenogears beeing episode 5. But, square didnt believe the series and the series creator left square and created monolith soft.
The series was then continue on Xenosaga, with the handle of Namco. The new series managed to retain the great storytelling but lacked on the gameplay department until episode 3. With low series sales already dooming the theird game to be unable to resurrect the series.
With Namco no longer supporting it, Nintendo came into the fray and monolith tried to once more reboot the franchise, this time into Xenoblade, and achieving great sucess. To the point where they were aquired by Nintendo and are now producing the latest entry into the series: X.
For series information i believe that despite what would official be said, Xenosaga episodes 1-3 are indeed the plots intended for Xenogears 1 to 3. With Xenogears 4 beeing the story reference in Xenogears with the previous generation. Beeing that Xenogears episode 7 is the only storyline not referenced in any game as of now.
From the ending of Xenosaga episode 3 you saw that there was definitly and interest in exploring the origins of the world portraid in Xenosaga and that is where Xenoblade comes in, beeing the unexpected entry in the series, lets call it Xenogears zero.
Status: Alive
Possibility of return: It already is, and under Nintendo's tutelage, the series is sure to keep on striving, even if it might further stray from the initial designs on the Xenogears saga.
Chrono series
Where did we go wrong with the Chrono series? The first a masterpiece, the second also a masterpiece but a fanbase unwilling to forgive that the second didnt soar the same heights than the first. This i think is what led to the dormant state of the series. Not only that but the creators of this game are great names in the industry. Those would probably be impossible to gather up again for a possible sequal.
Status: Very dormant if not dead.
Possibility of return: Lets be honest, its possible. But it requires square to give the get-go and invest on a different team than the original one. A revival is unlikely, but i wouldnt say impossible. The game has a great cult following, but if FFVII hasnt had its remake and its so heavily requested, what chance does the Chrono series have?