Detrimental effects and saving throws

[Omega Blue]

If I am under a detrimental effect, would increasing the relevant save force a new roll?

[Pigslayer]

Having high saves can cause you to be unaffected by a detrimental effect or reduce its duration. Only a few effects check against your saves every turn (most of those are mental). Raising your saves may cause the effect to fail its check.

[PureQuestion]

Saves are only checked when the status is applied.

[HousePet]

I think there are a few rare effects that do recheck every turn.
But most don't.

[Pigslayer]

The only ones I can think of are pacification hex, beckoning, and paranoia. Maybe some solipsist talents as well?

[Crim, The Red Thunder]

Doesn't inner demons? (and the tormentor thingy that Aletta uses?)