Like many companies operating in cyberspace, popular online securities brokerage Robinhood has fallen victim to hackers. According to a report published Thursday by Bloomberg and citing "a person with knowledge of an internal review," almost 2,000 accounts under the Robinhood Markets service were compromised by a recent spate of hacks.

The news follows another story Bloomberg broke last week about a series of hacks successfully targeting Robinhood clients. Five people said they were victims of this, and securities and cash were apparently looted in at least one instance.

A hooded hacker using phones and a PC.

Image source: Getty Images.

Last week's breaches prompted a raft of complaints from Robinhood account holders about the company's customer service. It does not presently have a contact number for this function. Following last week's hacks it sent notifications to clients with instructions for enabling two-factor authentication -- considered to be a far stronger security regime than a simple login and password -- on their accounts.

In response to Thursday's article, Robinhood said in an email, "We always respond to customers reporting fraudulent or suspicious activity and work as quickly as possible to complete investigations. The security of Robinhood customer accounts is a top priority and something we take very seriously."

Hacking has been an issue for securities brokerages since they first began online operations. Among other examples, TD Ameritrade -- which was recently acquired by Charles Schwab (SCHW -0.10%) -- suffered a database breach in 2007 that led to the theft of contact information from around 6.3 million accounts. In 2013, Schwab itself was the target, when a denial-of-service attack shut down its website for nearly two hours on a trading day.