From The Dim Future Wiki
A continuous effect is an ability of a card that effects cards within range of it constantly (instead of as a triggered ability). Continuous effects can have the forms:
- < card selection criteria> gains <ability or attribute>
- < card selection criteria> losses <ability>
In the "gains" form, any card that meets the criteria and that is within range of the card with this ability gains the described ability or attribute. In the "losses" form, the card that meets the criteria losses the specified ability. The checks to see if a given card is affected are done continuously.
Therefore, if a character is the source of a continuous effect and it moves, the set of cards that are affected by that ability immediately change. There is no chance to respond to that change, however you can obviously respond to the movement.