And the defeats to Raith Rovers in the Ramsdens Cup final and Dundee United in the William Hill Scottish Cup semi-final have also increased backing of the scheme.
The stand-off between King and the Gers directors has intensified after the club sent out renewal forms last week - before they published the outcome of their business review.
The South Africa-based businessman claimed that went against a gentlemen's agreement he had struck with the board after meeting them in Glasgow last month.
And he has urged followers of his boyhood heroes to withhold their season ticket money until they receive security over Ibrox Stadium and Murray Park.
The board has robustly rejected the 59-year-old Scot's claims - and revealed they have referred his explosive comments to their legal advisors.
The latest episode in the increasingly acrimonious off-field saga at Rangers has come as Ally McCoist's side has suffered back-to-back defeats in cup competitions.
And all of those developments have resulted in hundreds more Rangers supporters pledging to withhold their season ticket cash from the club.
Over 7,000 of them have now indicated their willingness on the Union of Fans website to pool their money in an escrow account set up by King.
"We have certainly had a boost in sign-ups over the last week or so," said Chris Graham of the Union of Fans earlier today.
"I am not quite sure if that is related to the team's results or if it is a response to the various statements that have come out from both Dave King and the board.
"But we have not been publicising or promoting the website due to the fact that we were hoping to engage in meaningful dialogue with the club.
"There has been a fair degree of disaffection with the way things have been going on the park, and the recent statements have raised the profile of the matter."
The Union of Fans - an umbrella group comprising six Rangers supporters' groups - is unhappy with the date of the season ticket renewal deadline.
For they believe it will not give many Gers supporters the chance to properly assess the findings of the 120-day business review conducted by chief executive Graham Wallace.
The club last week confirmed the eagerly-anticipated findings of the review would be made known to fans and shareholders tomorrow week.
Graham said: "The club have stated that May 6 is the deadline for season ticket renewals.
"But, if you are in the four-month payment plan, as many fans are, then you have to cancel your season ticket in writing before April 28 or the first payment will come off automatically.
"They are, then, effectively giving fans the weekend to decide whether they want to renew their season tickets after the publication of the results of the business review."
He continued: "The club is in full control of the whole process and can decide when they can release the results of the review. They have taken it forward four weeks. In my opinion, it is farcical they have left it as late as they have.
"They have moved the renewal dates forward. Generally speaking, in the past, fans had until the end of May. Even then you had until the middle of June to renew before your season ticket went elsewhere."
Graham and many of his fellow Rangers supporters have been concerned by the assurances given by the board over their future intentions for both both Ibrox and Murray Park.
And he believes that giving fans security over the stadium and the training ground for the duration of the domestic campaign in return for season ticket money is vital for the future of the club.
He said: "There are loads of variables in this situation. Ultimately, it is going to be played out in boardrooms and in the offices of institutional investors.
"All we can do is to give people options. We want safeguards that all Ibrox and Murray Park will be used for in future is for playing football.
"We just want Ibrox and Murray Park secure. When we asked for assurances we were told that the board was not looking at it 'at this time'.
"That is a situation that can change in one board meeting. I don't think we can rely on the board given some of the things that we were told at the AGM back in December. We are looking for more than words."
Graham added: "One of our fears is that people may decide they have simply had enough, become disillusioned and just walk away from the club.
"This is about giving people an alternative. If we can tell people that we have managed to secure the stadium and training ground for a year they will feel more comfortable putting their money in.
"I have no idea how many people will sign up for the trust.
"But even if there are, say, 1,000 or 2,000, why does the club not engage with us? It seems bizarre not to act even if a portion of your customers are taking this action."