The following are speculations and rumors and nothing confirmed, the only one that was for sure was that Disney was quitting on Power Rangers by 2010. These are rumored instances of when Power Rangers was 'almost canceled.'
By Season 3, Power Rangers' ratings started to decline but Toy sales remained high enough to make the show profitable to all the companies involved. It was said that Big Bad Bettleborgs beat PR in the ratings for a short time
. They then decided to change the name, suits, everything except most of the cast for Zeo and ratings were better.
The first half of Turbo had low ratings and sequel got mixed reviews and not a whole lot of profit, leading the crew to think their time was almost up. But the second half of Turbo had better ratings and led them to do In Space. They got Judd Lynn to lead the way for the second half, old plots were abandoned (like Divatox/Dimitria), no more Lerigot, and 4 new castmembers. I don't know if Fox Kids threatened them to cancel them or not.
A lot of evidence leads fans believe the crew thought Power Rangers in Space was the final season was because of the bringing together of old villains, the search of Zordon and of course the finale--that brought together Blue Senturion, Phantom Ranger, Gold Ranger and the Aquitar Rangers and the destruction of all known villains. But because of high ratings, the crew was led to make another season. I think by this season, they were expecting to just close up shop and wasn't threatened to be cancelled. Bandai did help with the budget for the Battlizer and continued to do so.
Lost Galaxy was also thought to be the last season, Saban was only producing Mystic Knights. Mystic Knights, the first live-action Saban did that had no existing Japanese Tokusatsu footage was to have a second season but they opted not to do it and all the budget was allocated to the second part of Lost Galaxy. Ratings were passable for Lost Galaxy so they continued. They had a lot of budget for Lightspeed, ratings were great for Lightspeed and Time Force. To give you an idea of the budgets, I made the chart above. 1995-1996 and 1997-1998 were the only two times they had 3 shows filming at the same time: Season 3 of MMPR, VR Troopers Season 2, and Masked Rider; Power Rangers in Space, Beetleborgs Metalix and Ninja Turtles: Next Mutation. While Turbo, Space and Lost Galaxy ran in the course of one year and not between two years, Beetleborgs, Mystic Knights and Next Mutation ran between two years, from September to Spring. Also, Beetleborg monsters were used for seasons of Power Rangers starting with 'In Space' and also Mystic Knights.
Rumor is that Jungle Fury was going to be the last season because it was the last one Disney really promoted and it was the last one to air on Toon Disney. When Toon Disney became Disney XD, Power Rangers was knocked out and new episodes only aired on ABC. RPM got no promotional photos like past Disney seasons, almost no promotion, very little merchandise (save for the toys) and it was rumored that the only reason they did RPM was because Bandai released the toys. Judd Lynn swears Disney did care about PR during RPM, I believe at least at a production standpoint. Even though not officially 'canceled' since MMPR reversion aired in 2010, production did stop in New Zealand and Disney was in conversations to sell it back to Saban. It is rumored Bandai helped with the budget, not for new Rangers or Battlizers, just for budget all together. So Power Rangers was never officially canceled but ratings did get low and there was rumors of it being 'the end.' The closest thing to being 'canceled' was the 5 months between the reversion being off the air (in September) to when Power Rangers Samurai premiered in February.
Mystic Knights: Battle Thunder was the planned second season of Mystic Knights but never happened. Of all the Saban shows, Mighty Morphin Power Rangers to Lost Galaxy are available on DVD, so are VR Troopers, Beetleborgs and Ninja Turtles: Next Mutation. It has not yet been announced if Mystic Knights or Masked Rider will be DVD yet, but I suppose they will be some day.