The East Dunbartonshire MP has faced questions over what action she took after becoming aware of allegations against the peer.
Senior Liberal Democrat sources said Ms Swinson was being put in the spotlight because she is a woman.
One said: "The attitude, that she should have done more because she is also female, has been very sexist."
Meanwhile, The Herald has learned that LibDem members were asked to report any further incidents of harassment even after Treasury Chief Secretary Danny Alexander challenged Lord Rennard.
The party faced fresh accusations of a cover-up after Nick Clegg appeared to admit for the first time that alleged misconduct had played a part in the peer's 2009 resignation as party chief executive.
At the time, the LibDems put the decision down to ill health, but Mr Clegg admitted the allegations were "in the background".
In another significant shift in the party's position, its president, Tim Farron, warned there was "every chance" it had let women down.
One of those at the centre of the scandal, former Aberdeen councillor Alison Smith, also challenged the party's version of events, saying she had always made clear she was willing to take her claims to the police.
Mr Alexander confronted Lord Rennard in 2008, after Mr Clegg's office heard rumours of accusations against him.
The peer, who strenuously denied and still denies all the allegations, was told any such behaviour would be unacceptable.
After the meeting, however, some LibDem members received emails asking them to report any future alleged abuses.
The message also reassured them that Lord Rennard had been challenged over his alleged misconduct.
A spokesman said the message was sent "after Danny spoke to Lord Rennard".
It was sent in late 2008 by former LibDem campaigns officer Duncan Barrowman.
Aides to Mr Clegg said Mr Barrowman had acted because he had been contacted by some of the alleged victims and wanted to reassure them action had been taken.
Among those who received the email was the leader of the Welsh LibDems, Kirsty Williams.
The Scottish LibDems said no-one in the party north of the Border had received such an email.
Pressure has been mounting on Mr Clegg following reports he was warned in person by one of his former colleagues.
Former MP Sandra Gidley said she had a face-to-face discussion with Mr Clegg after he was elected leader in 2007.
But Mr Clegg said she had raised the issue only in "general terms".
Of Lord Rennard's departure in 2009, he said: "Of course, these things were in the background but his ill health was the immediate reason why he stood down."
One of the party's most senior figures rushed to the defence of the peer.
Baroness Williams said he was a very fine man and that the situation had been "hopefully exaggerated".
She also described the House of Commons as a "very bullying place, a masculine culture".
Mr Farron earlier admitted there was "every chance" the Liberal Democrats had failed women who raised concerns about the peer's conduct and the party needed to "take that on the chin".
The Tories also broke Coalition ranks to attack the LibDems on the scandal.
Conservative Business Minister Michael Fallon said the party had failed to come clean about what had happened.
He said: "One of the reasons the LibDems are in trouble is they haven't really been straight about this."