like a broken record

sound/be/feel like a broken record (to say the same thing over and over again) — повторять одно и то же снова и снова, как пластинка, которую заело; твердить что-л. как заезженная пластинка; повторять что-л. как заведенный

Telling someone that they sound like a broken record is saying that you’re tired of hearing them say the same thing again and again. If someone tells you that you sound like a broken record, it’s time to change the subject.

Example 1: He's always complaining about the way she treats him. He sounds like a broken record! (McGraw-Hill Dictionary of American Idioms and Phrasal Verbs)
Example 2: I hate to sound like a broken record, but we just don't have enough people on the payroll to work effciently. (McGraw-Hill Dictionary of American Idioms and Phrasal Verbs)

a broken record — испорченная пластинка, заезженная пластинка
be (such) a broken record (someone who keeps annoying you by repeating the same thing)

Example 1: I mean, I may be a broken record, but I just know too many kids who had famous parents who, for one reason or another, just didn't do much with their lives. (COCA)

See also:
[not hear the end of sth]
[уши прожужжать]
talk [nineteen to the dozen]
[run off at the mouth]
[on one's soapbox]
[in one’s element]

Общее значение:
talk so much that the listener is tired of it

Just like CDs, phonograph records could get scratched, which would cause the record to miss or jump over part of a song. Scratches could also make the needle (or stylus) stay in the same groove and get stuck on certain words in a song, playing them over and over again.