I also live in an HOA and understand your frustration.
First, I would look thru your HOA Declarations. I am sure that there is a paragraph somewhere in there about Nuisances. This falls under this and the HOA can (and should) send out a violation letter each time you report the issue. If they fail, you can sue the board for not enforcing the Declarations of Covenants, Conditions and Restrictions for your community (and receive a judgement requiring enforcement). This is the same as any other violation in your neighborhood.
Second, the police should enforce the county/city noise ordinance. From past experience with this issue, you should keep a log and continue to call the police each time they are blasting the music. Demand the police enforce the oridinance. If they don't, call their supervisor the next day. Either way, you can use your log to demonstrate the ongoing problem.
I think the suggestion of talking to them is a great idea, however I would understand if you did not want to do it. I have had both good and bad experiences talking with neighbors about these type of issues.
Good luck and I hope you find a way to resolve it !