Does prayer cease to be an atonement for sins if songs include prohibited musical instruments, which are considered major sins, due to not abstaining from major sins? And if musical instruments are considered minor sins, how often must they be repeated to become a major sin?

Listening to musical instruments (ma'azif) is forbidden. The fact that a sin is minor does not permit one to commit it, for persistence transforms a minor sin into a major one. Persistence is an act of the heart and is not determined by the number of times; it is the firm resolve of the heart to continue an act and not desist from it.

The persistent one is doomed. Whoever intends not to repent is persistent. However, whoever intends sincere repentance exits the state of persistence.