By the time Scrimgeour took over as Minister, the Dementors had long-since changed their allegiance to Voldemort. During the events of Book 5, we see a large scale break-out of Death Eaters from Azkaban, aided by the Dementors.
Although the Ministry didn't acknowledge this change of allegiance in Book 5, they eventually did by the end of the book. Following the battle at the Ministry, Lucius Malfoy and other Death Eaters were imprisoned and sent to Azkaban, which was guarded by the Dementors (known allies of Voldemort at this point) again.
....said Fudge, looking tired and flustered as he addressed reporters. "It is with almost equal regret that we report the mass revolt of the dementors of Azkaban, who have shown themselves averse to continuing in the Ministry's employ. We believe the dementors are currently taking direction from Lord-- Thingy.
'The dementors have left Azkaban,' said Malfoy quietly. 'Dad and the others'll be out in no time ...'
'Yeah, I expect they will,' said Harry. 'Still, at least everyone knows what scumbags they are now--'
Both quotes are from OotP, Chapter-38, The Second War Begins
My question is, why did neither Fudge (post the revelation) or Scrimgeour after taking over as Minister of Magic, not bother changing the guards for the imprisoned Death Eaters? Why would the Ministry risk imprisoning them at a place which was guarded by Voldemort's known allies, especially since the rest of the wizarding world was also aware of this information at that point? (Considering the Ministry was always trying to save face with the general wizarding population)
I get that Fudge who was already a sloppy, non-proactive leader, was probably in pieces and hit rock-bottom post the sensational Voldemort revelation. But wouldn't Scrimgeour, (who seems a lot more sensible, and was someone who didn't take Voldemort lightly, acc to Dumbledore) have most definitely acted on this?