If a group - such as NRA or AIPAC - have the ability to prevent a political candidate not sufficiently aligned with either group’s demands from being elected (let’s hope average Doper can do their own Googling to determine this even though by now even birds on the trees sing about it) what happens is that candidate who was prevented to win by intervention into political process (i.e. election) was effectively prevented to represent his/her electirate because all other politicals positions of the candidate are ignored such as his/her stand on taxes, local infrastructure, education, healthcare and similar issues affecting his electorate in favor of one single issue that may or may not be in top 5 issues affecting given electorate. But, what happens, due to concentration of power in groups such as AIPAC or NRA, is that election process becomes bent by ideological stance and as a result electorate is not represented because the groups like this use resources from other places, perhaps even foreign resources to win given electorate.
That is a clear violation of representative democracy. Provided, of course, that we share the same definition of what representative democracy is as something tells me that that definition will change for some to suit their stated conclusion that groups like this actually operate within the idea of “representative democracy”.
In Soviet Union and many Iron Curtain countries political process had their group that operated isomewhat similar fashion; there was also ideological bent present - there was a group in every electorate that measured alignment of a candidate to the policies such as private vs. state property and this group was essentially vetting each candidate. So, it’s not that SU did not have a political process or that there were no candidates with fresh ideas - it’s just they didn’t pass the smell test of a powerful group. As the time goes by the pie will get ever smaller and at one point there will be no pie left. That’s what happened in SU - it’s not that their system was all that bad, they knew how to make stuff - they ran out of money to go around for special interest as all the good people who wanted to contribute were weeded out and only apparatchiks left.