A motion from Councillor Donald Moffat, leader of the opposition SNP group, which called for a return to a committee system in which all 34 councillors are involved, was defeated by 17 votes to eight at the full council meeting.
"The vote rather proves our point," said Councillor Moffat. "Some elected members are disbarred from taking part in debates on important matters like education, social work and roads, and this is bad for democracy.
"Only when the full council meets monthly do we have our say and what happened today is typical because we are simply outnumbered."
He was referring to the "executive and scrutiny" format, introduced in 2001. The executive, chaired by leader David Parker, comprises 12 councillors with special departmental responsibilities drawn from the ruling adminstration of 11 Tories, 10 Lib Dems and four independents.
The opposition consists of six SNP councillors, two from the Borders Party and one non-aligned independent (David Paterson of Hawick).
Just two members of the opposition (Mr Moffatt and Nicholas Watson of the Borders Party) are on the nine-strong scrutiny panel which holds the executive to account for its decisions and actions.
"The conspicuously few times when executive decisions are successfully called in shows that scrutiny is not a real forum for debate while, given the huge majority of the ruling administration, the full council does little more than rubber-stamp decisions taken by an elite few," said Mr Moffat.
He said he believed opposition councillors should, on a proportional basis, be involved in committees covering key functions, such as education, with the full council as the ultimate decision-maker.
Mr Parker opposed the return of committees, claiming they would be more expensive and result in slower decision-making. He was satisfied the status quo was, indeed, democratic.
"Our current system has been in place since 2001 and it has been praised routinely by external auditors and independent reviews," Mr Parker said later.
"Our structure has been held up as an example of a decision-making process which makes good efficient decisions and a number of other councils have visited the Borders to see how we do things.
"The old committee system may have been appropriate a number of years ago but the world and the council have moved on and those who more strongly advocate the system were around in local government when it was a very different place.
"We must remember that 80 per cent of the decisions under the old committee system were for noting and the decisions that they could make on their own were routinely overturned by the policy and resources committee or the full council. It would strike me that returning to an outdated, costly talking shop is not what we need right now.
"If you look carefully at our external audits and inspections, none of them have ever criticised the political decision-making processes at SBC.
"However, it should be remembered that in the past, at the height of the education overspend, the committee system and the education committee were held up as contributing factors to the cause of the problems we faced."
But Mr Moffat said: "We accept we do not have enough numbers to wield power, but our members have some good ideas, which could improve services and even save the council money and committees would at least allow us to engage meaningfully.
"All we want is the right to take part in debates before decisions are made. It is outrageous, for example, that the education executive has church representatives, but no elected member from the opposition.
"This is the third time in as many years the SNP has called for a return to committees and we will continue to press for fairer representation, both for ourselves and the people who voted for us."
A discussion about a report on a revamp of SBC's five area committees was deferred until August. The report, which follows consultation with the public, recommends retention of the committees in Berwickshire, Cheviot, Eildon, Tweeddale and Teviot and Liddesdale, but with a boosted membership to include, apart from ward councillors, a representative from each community council (up to 21 in the case of Berwickshire) who will have full membership.