Two million customers at the taxpayer-backed bank, which includes NatWest, have the app on smartphones and tablet computers, and many took to Twitter to express frustration after they were unable to use it to check their money.
RBS apologised over the glitch as it scrambled to restore the service. A spokesman later said the app was working again. It appeared to have been out for around two and a half hours.
The failure follows an IT fiasco last summer that saw payments go awry, wages appear to go missing and home purchases and holidays interrupted, and has already cost the bank £175 million in costs and compensation.
The setback is the latest bump in the road for RBS, which is 81% publicly owned, as hopes rise that it can soon be returned to the private sector after being rescued at the height of the financial crisis.
Its latest annual results saw it record losses of £5.2 billion, driven by a £390 million settlement for rate-fixing, £1.1 billion provision for mis-selling, and the IT problems of June and July 2012.
It has been encouraging customers to use the technology, sending out tweets such as one two days ago which read: "Is it easy to pay someone with your bank's mobile app? It's simple with RBS."
Frustrated customers described how they tried to access the app but were told there was no internet connection - although other apps were working. One said he had been logged out in the middle of a transaction. He received a response from RBS apologising and telling him to "try again later".
Another Twitter user wrote: "RBS app decides to play up on the 1 day of the month I need to know whether it's payday or not." A further tweet said: "Pointless having the #rbs app on my phone because it hardly ever works."