Is there a way to continue a project if you loose power and easel thinks your project is complete?
Unfortunately there is not. You will need to rerun the project from the start.
Easel do not support “resume” on an aborted carve.
If you have a known reference point (like homing switches or triple edge finder) you can recarve from the beginning. Easel allow for up to 200% feed speed increase which will cut down the “airtime”.
Another option is to use the same gcode file, but manually edit away the already carved section. This require some gcode knowledge, or good instructions to do with comfort 
Depending on the design, you may be able to block out already carved parts by placing a square above, set to 0 depth.
Thank you.