Saudi Crown Prince Mohammed bin Salman visited Kuwait last month to discuss a resumption of oil output from the zone.
But the sources, who asked not to be identified as they are prohibited from discussing the issue publicly, said the talks failed to move the two countries closer to a deal as Kuwait resisted Riyadh's push for greater control of the fields.
"It did not go well because Kuwaiti sovereignty is non-negotiable," one source told Reuters.
Riyadh does not want Kuwaiti laws to apply to U.S. oil major Chevron, which operates the Wafra onshore field on behalf of the Saudi government, the source added.
Another source said Saudi Arabia wanted a bigger say and more control in running oil operations in the zone.
Prince Mohammed met Kuwaiti Emir Sheikh Sabah al-Ahmad al-Jaber al-Sabah and Crown Prince Nawaf al-Ahmad al-Jaber al-Sabah but the visit was cut short from the originally planned two days to just a few hours on the night of Sept. 30, the sources said.
Adding to the political friction were tensions between the two countries over the embargo of neighbouring Qatar and diverging views on relations with Saudi Arabia's arch-foe Iran, the sources said. Kuwait is trying to mediate the embargo, which is being led by Saudi Arabia and the United Arab Emirates.
Saudi Arabia, Bahrain, the UAE and Egypt cut diplomatic, transport and trade ties with Doha last year, accusing it of financing terrorism. Qatar rejects the charges.
Kuwait has sought to maintain neutrality, although the Emir's efforts to mediate the rift have had little success so far.
Kuwait, which has a sizeable Shi’ite Muslim minority, has also maintained dialogue with Shi’ite Iran. Saudi Arabia and Iran back opposing sides in civil wars in Syria and Yemen.
In a move that may further complicate relations with Riyadh, Kuwait this month signed a defence cooperation plan with Turkey in what it said was meant to strengthen bilateral ties.
Turkey has sided with Qatar in the Gulf row and its relations with Riyadh have been strained due to Ankara's close ties with Iran.
"The (regional) situation is not stable, so every country should think how to protect itself," Saleh Ashour, a member of the Kuwaiti parliament, told Reuters.
COSTLY IDLE WELLS
Oil output in the Neutral Zone, which dates back to 1920s treaties establishing regional borders, is divided equally between Saudi Arabia and Kuwait.
The Wafra field is operated by state-run Kuwait Gulf Oil Co and Chevron on behalf of Saudi Arabia. The Khafji field is operated by state oil giant Saudi Aramco and Kuwait Gulf Oil.
Tensions have been simmering since the last decade, when Kuwait was angered by a Saudi decision to prolong Chevron's Wafra concession until 2039 without consulting Kuwait.
In 2014, Saudi Arabia closed Khafji, citing environmental issues. In 2015, Chevron shut Wafra citing difficulties in securing work permits and materials.
"Saudi Arabian Chevron is focused on supporting operational activities to maintain readiness for production restart when that time comes," a Chevron spokeswoman said.
"Obviously a restart depends on the discussions between the two countries. But we’re ready. We are maintaining the equipment, we have put a lot of effort into keeping the pipelines in shape and keeping the key wells in shape."
Shutting output is expensive because it requires investments of tens of millions of dollars per year for maintenance, sources familiar with field operations said.
The Neutral Zone "is the single biggest asset in the world which was deliberately stopped and hasn't been producing for three years", one of the sources said.
"The more the restart is postponed the more it will cost to maintain it. And the more problematic it might be to restart the fields quickly and fully," he added.
Industry sources from both countries say that though Khafji and Wafra are not linked geographically, an agreement to bring one field back online would be tied to the other.
(Additional reporting by Ahmed Hagagy in Kuwait; Editing by Dale Hudson) ((firstname.lastname@example.org; +971 562 160 434; Reuters Messaging: email@example.com ; Twitter: https://twitter.com/Rania_ElGamal))