It is claimed hundreds of people are waiting for a SPECT brain scan at the Southern General Hospital in Govan.
The scan can highlight the origin of seizures, allowing corrective surgery to be performed in severe cases.
Problems are thought to have arisen after a new £350,000 scanner was installed this year. Patients have been told engineers are working on the machine.
NHS Greater Glasgow and Clyde said the delay was caused by technical issues and apologised to patients waiting for scans. But they were unable to say when the scanner will be operational.
The only other UK city offering the scan on the NHS is London. NHSGGC said patients would not be referred there because of "lengthy" waiting lists.
Charity Epilepsy Scotland has expressed concerns about the resulting "gap" in services and waiting lists.
It has asked bosses at NHSGGC what alternatives are being considered for priority cases, such as referrals to other hospitals.
Among those waiting for a scan is the daughter of Colin Downie. She was referred in March after being diagnosed with epilepsy eight years ago. Her condition has now become chronic.
Mr Downie, 48, a train driver from Ayr, said: "We kept asking, then I got a letter saying the scanner would be up and running by July.
"We were then told it would be ready by the end of August, and that didn't happen. I phoned again in September. We were told they were calibrating the machine. We got the same message in October. They are now saying it won't be operational until the New Year. We have heard there are hundreds of people waiting for the scan."
The scanner is also used to diagnose Alzheimer's and stroke.
Figures show there are about 54,000 people living with epilepsy in Scotland and surgery may be recommended for patients whose seizures can't be controlled with medication, about one third of the total.
A spokeswoman for Epilepsy Scotland said: "We received a commitment from NHS Greater Glasgow and Clyde to replace the scanner.
"It is disappointing there is now a gap in resuming this important service."
A spokeswoman for NHSGGC said: "In May this year we invested £350,000 in a new replacement IctalSPECT scanner. It needed to be custom built, a process which took some three months to complete by the manufacturer in Hungary. The scanner was then shipped to Glasgow, however, while going through our rigorous acceptance testing process, technical issues were identified.
"With the manufacturer, we are working to address these and get the scanner on-line as soon as possible."