Dennis, a 25% shareholder in McLaren Group who wants to take a controlling interest in the company, sought an injunction in London on Friday.
The failure casts further doubt on the 69-year-old's position after shareholders told him last month they would not renew his contract for 2017.
McLaren refused to comment when approached by BBC Sport.
The Bahraini royal family owns 50% of the company through their Mumtalakat investment fund, with the remaining 25% owned by Mansour Ojjeh.
He is the long-time business partner of Dennis, but the pair have had a difficult relationship in recent years.
Dennis has been seeking investment to enable him to take his shareholding over 50% and give him total control of the company.
An initial investment plan from a group of Chinese investors fell through some time ago following a weakening of the country's economy.
Dennis sourced a second Chinese consortium, only for the Bahrainis and Ojjeh to decide not to sell because they did not want Dennis to take too much control.
Ojjeh and the Bahrainis now want to remove Dennis from power by suspending him from his position with immediate effect, pending the expiration of his contract which is believed to be in January 2017.
If they follow through on their threat, the Briton's reign as the head of one of Formula 1's most successful teams will come to an imminent end.
But as things stand, Dennis remains chairman and chief executive officer of McLaren Group.
Dennis took control of McLaren in 1981 and led the company to 10 drivers' titles - with the likes of Niki Lauda, Alain Prost, Ayrton Senna, Mika Hakkinen and Lewis Hamilton - and seven constructors' titles.
However, the team have struggled in recent years and achieved an all-time low of ninth place in the constructors' championship in 2015 following the start of a new engine partnership with Honda.
Although McLaren and Honda have made progress and are lying sixth in this year's championship with two races to go, Ojjeh and the Bahrainis have concerns about the direction of the company under Dennis.
Among their concerns is the failure of Dennis to secure a new title sponsor following the exit of mobile phone giant Vodafone at the end of 2013.
McLaren chairman Ron Dennis has failed with a High Court bid to prevent his fellow directors suspending him.