As long as you don't lose any of the broker's money, the broker couldn't give a rat's a$$ how much you lost very much like a casino wouldn't care how much you lost playing their Russian Roulette.
Of course brokers monitor client losses. They will call you if you in in violation of margin requirements
Many brokers do in fact monitor accounts for losses. As other posters have said, they won't stop you as long as margin is not involved. Here is an example letter Fidelity sends out when an account loses a substantial amount in a short period of time:
Outside of margin, looks like they care because they want to hook you up with managed money and give you "advise" for a fee LOL.
it all depends on the broker's approach to their work, many often monitor all the transactions of their traders, and the general work of each trader