On Friday Andy Green, one of the two candidates for president in 2017, announced his withdrawal from the race, also saying he would be "calling upon the CIPR to conduct an urgent review of the election process".
On Monday, the institute said it would form an independent panel to review complaints received about the election, which was left with just one candidate following Green's withdrawal.
PRWeek has since seen emails from two members of the CIPR detailing complaints that have been made since Friday and rejected by CEO Alastair McCapra, who is acting as the returning officer for the election.
The first member's email was addressed to CIPR council members and described the member being "extremely concerned at how CIPR HQ has managed this election" and that the situation was "an absolute shambles".
The member said that, prior to his public withdrawal, Green had been told by the CIPR that he had been disqualified for following outdated rules that were incorrectly displayed in one place on the CIPR website.
The member also said that the complaint made to McCapra was rejected, but that they felt the "only fair thing" would be for nominations to be reopened. The member - who was not responsible for the email being shown to PRWeek, but asked to remain nameless when contacted - also said they had written the private email rather than making a public statement because they "loved the CIPR" and wanted it "to grow and have strong reputation".
A separate complaint from another CIPR member also called for nominations to be reopened, also pointing out that an incorrect version of rules appeared on the CIPR website. In rejecting the complaint, McCapra wrote to the member saying he was "not aware of any action taken by either candidate which, while disallowed under the current regulations, would have been permissible under the previous regulations".
Where a complaint has been rejected by the returning officer, it can be appealed.
A spokesman for the CIPR said: "Any complaint that has been ruled on and rejected by the returning officer and subsequently appealed will go on to the independent panel - that is why it is there. The panel may see a rerun of the election as necessary."
- This story and the headline originally said one of the individuals quoted was a CIPR council member. This was corrected shortly after publication.