Last month, a bidder wanting to provide the University Hospital of Hartlepool's fertility services was rejected, despite already running services there.
The borough's council said it had not been told why.
The area's clinical commissioning group (CCG), which had said it could not recruit enough staff to keep the unit going, has been approached for comment.
Care Fertility, which operates 15 clinics across Britain and supports fertility services in Hartlepool, said in January it was "disappointed not to be awarded the contract".
Hartlepool and Stockton-on-Tees CCG said the bids it received had not met "the benchmark requirements".
At a meeting on Thursday Hartlepool councillors voted to request the CCG put it back out to tender.
Audit and governance committee chairman Ray Martin-Wells said the committee could not "understand why a company with a proven track record which is already providing a service at the unit and at 15 other fertility units across the country is deemed to be not good enough by the CCG".
The committee also decided to seek further legal advice.
Last year Hartlepool Council was granted a High Court injunction stopping a planned closure, after which it was announced an alternative provider would be sought to run fertility services, including IVF.
Health managers wanting to close a hospital fertility unit are being asked to put the service back out to tender.