You use a fig with perplex to modify a flier, and then have said flyer hypersonic carrying the perplexer. Does the perplex still count while the perplexer is off map?

Perplex
Give this character a free action to modify by +1 or –1 any combat value of a target character until the beginning of your next turn. A character using this power must be within range (minimum range 6). If a target character is damaged or healed, the effect of Perplex on that character ends immediately.

As long as the Target wasnt damaged or healed and the Perplexer didnt lose the power you still get the modifier.

A character never leaves the map during HSS. A carried character is in the square it began the action in until the action is over, then is placed next to the HSSer after the movement is resolved.