By Anna Irrera and Abhishek Manikandan

(Reuters) - Fintech startup Robinhood Markets Inc said on Tuesday its free stock trading app is up and running again after a second straight day of outages.

"Robinhood is now fully restored ... we will work diligently to provide the level of service you deserve," the company said in a tweet https://twitter.com/AskRobinhood/status/1234884989189124096.

The Menlo Park-based company had fixed an infrastructure issue on Monday night that had caused a day-long outage preventing customers from trading as stocks surged following last week's slump. It experienced technical problems again early on Tuesday, before getting the app back into service.

While issues on Tuesday were resolved more quickly, customers again criticized Robinhood on social media. Many lamented that they had missed out on significant market moves and some threatened to switch brokerages.

"Can someone explain how I can transfer my stocks to another broker rather than cashing out," one user asked on Twitter.

"Very frustrating given two important trading days in a row," wrote another.

The first outage came on a day of high trading volumes as Wall Street rebounded from last week's sharp sell-off triggered by coronavirus concerns. The Dow Jones Industrial Average surged over 5% on Monday, while the S&P 500 and Nasdaq each jumped more than 4%.

On Tuesday U.S. stocks fell in volatile trading after a half percentage-point interest rate cut by the U.S. Federal Reserve.

Robinhood is notifying customers on how to discuss possible compensation for being unable to trade on the app, said a spokeswoman for the company, which is popular among millennials.

Robinhood, founded in 2013, has been looking to offer financial services besides stock trading, while other brokerages have slashed their fees making the market more competitive. Other fintechs such as Square Inc have also recently started offering free stock trading.

(Reporting by Abhishek Manikandan in Bengaluru and Anna Irrera in New York; Editing by Ramakrishnan M. and Richard Chang)