As a preface to this question, I'm asking this under the assumption that Star Lord uses both of these items very regularly and as such they are subject to wear and tear.
We can see that the cassette player is in his pocket during that whole scene right at the start when he's fighting Korath The Pursuer and when he's bouncing around inside his ship shortly after.
Maybe if they were constructed from the hardest material in existence, I could believe they would survive, but they're made primarily from plastic and some small metal parts. It would be reasonable to assume that as a space pirate / superhero, he and his belongings might sustain physical injury / damage more often than perhaps you or I.
I'm assuming / hoping alien tech is involved, because that would be pretty cool.
Is it ever addressed in or out of canon?
A couple answers have been posted explaining the best way to repair a damaged cassette tape or walkman. Which isn't really an answer to this question.