If you would Accelerate it out of the deck, instead discard the next Stage II card underneath it (or the top-most Stage III card if there are no Stage II cards left).
Visions of a Shifting Future can't bury it to the bottom of the deck (since it's specially placed during Setup), but can shuffle it to take a chance at delaying it.
This can happen, e.g., if the first part of Indomitable Claim reveals an Element on a Presence track, or if the land gets Blighted and the card is Aid from Lesser Spirits.
Likewise if you lose Elements in the middle of resolving the Power, you may lose further thresholds.
While this tends to be pretty obvious when the cost is paying Energy, it's less clear if the cost is performing some other effect, like discarding a card or removing Presence.
While you must be able to pay the cost in order to get the bonus, ongoing effects can alter the final result of the cost being paid. For example, you can successfully pay the cost of "Destroy 2 Presence" even if Flowing and Silent Forms Dart By will end up saving that Presence from destruction if you do so. On the other hand, you can't attempt to pay the cost with Presence under Absolute Stasis, since that Presence only exists for Victory/Defeat – it doesn't exist as far as the Event is concerned. Tags: Action Modifiers, Flowing and Silent Forms Dart By, Absolute Stasis (Fractured Days Split the Sky), Turmoil's Touch (Wandering Voice Keens Delirium), 11 more...