The computer glitch, which was is now fixed, prevented some people from filing claims.
ESC spokesman Andy James said the commission's computer servers handled more than 106,000 transactions Monday, also a one-day record.
A phone line problem developed Sunday when 74,000 people tried to access the system.
The ESC fixed that problem, and thought it also had fixed a separate problem caused by too many people filing claims. However, the system failed again Monday when about 55,000 people tried to file.