How long do passion flowers stay open?
Thereof, do passion flowers only last a day?
A Passion flowers are the flowers of the climbing woody shrub Passiflora caerulea. You don't say where or how it is growing, but they are not wholly hardy and are likely to suffer - if not die - in anything but a very protected spot in a normal winter. Finally, remember that passion flowers only last one day.
Considering this, will my passion flower come back?
If you see green, it will come back. This past winter was hard on plants in many areas so some plants may have died back to the roots. It sounds like this has happened with your passion vine. But it will recover quickly of the roots are still alive.
Passion flowers usually don't need much attention to deadheading and pruning. You can remove spent flowers to keep the plant tidy and pruning should be done in early spring to keep an aggressive plant in bounds.