Student Juswinder Singh, from India, says he has been trying to lodge his visa application without success since Monday.
"It just keeps saying the application cannot be accepted," Singh said.
"INZ should go back to Third World service of having face-to-face staff if they cannot keep up with technology."
Walter Stone, a licensed immigration adviser from Eagle Migration, said the agency's online system has been "very problematic" since the start of the week.
"It keeps rejecting application uploads or fails to allow data entry for online temporary application," Stone said.
"It's now day four, and they still don't seem to be able to solve it."
The Government had committed $90.5m to upgrade the computer systems at INZ, aimed to improve efficiency and reduce operating costs.
In May, a crash of the agency's global Advanced Passenger Processing system caused lengthy delays at airports here and in Australia.
June Ranson, NZ Association of Migration and Investment chair, said INZ's system for online applications "lacked reliability" and has been faulty for some time.
"Some applicants had to edit their passport photos many times in order to meet the online system for acceptance, but end up having to send their actual photos separately," Ranson said.
She said the system was also asking for X-rays and medicals to be submitted by the applicants, but that isn't possible because it was the agency's panel doctors who release these reports.
Dunstan said in the last couple of days, more than 1700 applications have been successfully lodged, which was approximately 500 more than its usual two-day total.
