Robinhood says it has strengthened its infrastructure, and is looking to strengthen its relationship with some clients after recent outages.

On Monday, the trading start-up emailed customers who said they were affected by tech glitches that caused them to miss out on a historic market day. A Robinhood spokesperson told CNBC the dollar amount would be determined on a case-by-case basis.

"We'd like to start with the apology you deserve: We're sorry for the recent outage on our platform. Your support is what helps us democratize finance for all, and we know we owe it to you to do better," the company said in an email to some Robinhood users. "An apology alone won't rebuild your trust in us. Instead, we hope our actions will."

The trading app said it was experiencing technical issues that kept it offline for nearly two full trading days earlier in March. As a result, Robinhood clients missed out on the biggest one-day point gain in the Dow Jones Industrial Average in history.

Robinhood was valued at $7.6 billion after a its latest funding round last year led by DST Global. Venture capital firms like New Enterprise Associates, Sequoia and Ribbit Capital are also investors. The start-up has ushered in 10 million — mostly millennial — traders by offering free equity, options and cryptocurrency trading.