@Sweet_Seats the title makes sense.
The word 脈 (miyaku) can be used in the sense of "hope".
脈がある (miyaku ga aru) can be translated "there is (still) hope".
In the same way, 脈のない彼女 can be translated as "hopeless girl".
This makes sense in two ways:
1. she's mentally affected by her immortality, which excludes her from being part of human society.
This is why she's hopeless in everything she persuades, especially her romantic advances onto the main character.
2. Immortality is philosophically speaking often considered as "the greatest curse" for any being.
This is true for especially European culture, where the Graeco-Roman gods were the personification of decadence
as they had to do something to keep them entertained in their everlasting existence.
Their evils were even emptied onto humanity (compare to the story of Pandora and the jar containing all evils),
so they are in fact a byproduct of godly existence.
Humans in contrast are limited by their mortality, which is why they try to become immortal by their deeds and legacy.
This is what kept them sane (memento mori), creating all we have nowadays through the laws of cause and effect.
In the end, a person that is no longer bound to the rules of cause and effect by being immortal will become what we consider decadent and insane. In short a "hopeless" person.