Suspend works in two phases. First, you exile the card and put the specified number of time counters on it. Then, at the beginning of each of your upkeeps, you remove one time counter. When the last time counter is removed, the game triggers an ability that lets you cast the spell without paying its mana cost (CR 702.62c).
Importantly, you don't choose to cast it from exile at that point in the normal sense — the triggered ability instructs you to cast it immediately, and you must do so if you are able. This cast happens during your upkeep step, which is an unusual timing window (CR 702.62d).
If you somehow cannot cast the spell at that moment (for example, a rule or effect prevents it), the card simply remains in exile with no counters on it. It is not lost permanently, but it won't be cast automatically again without another effect moving it.
Example: You exile Ancestral Vision with suspend (it enters with 4 time counters). Four turns later, on your upkeep, the last counter is removed. The triggered ability fires, and you cast Ancestral Vision for free — no blue mana required — during that upkeep step.
Key rules references: CR 702.62c covers removing the last counter and casting the spell; CR 702.62d specifies the timing (upkeep) and the 'cast without paying its mana cost' permission.
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