The only way the few remaining humans can survive the Vampire Apocalypse is by continually staying under the sunlight – but fuel, resources and transportation are running low.

I take it that the vampiric apocalypse hasn't happened yet. Staying under the sunlight or staying in the sunlight? What does low fuel, resources and transportation have to do with it? You could try and give it that personal touch.

Good idea for a story, but I agree with Karel that specifying the protagonist would increase impact.

I'd re-word the logline to make it less clunky. Maybe something like: "[Human survivors/protagonist] of the Vampire Apocalypse need[s] to stay out in the sunlight-- but fuel and resources are running low as darkness sets in."

Just a suggestion.

I can see an updated OMEGA MAN (or I AM LEGEND) but the logline needs to give me what is unique about this particular movie.

Also, specify who is the main character. A "few remaining humans" is too generic for an audience to have any anticipation of empathy.

Finally, it reads like an open-ended premise. They will have to continually stay under the sunlight.

Can you give us a deadline? How would an audience visualise a positive outcome? Then, this could be the goal for the main character(s).