The political down time over summer can be something of a respite for an embattled government. But for Scott Morrison, it has just brought more setbacks. The weekend announcement by cabinet minister Kelly O'Dwyer that she will leave parliament at the election is the latest and most serious.

O'Dwyer says she wants to see more of her two young children, and would like to have a third, which involves medical challenges.

Her decision is understandable. The first woman to have a baby while a federal cabinet minister has been juggling an enormous load.

But with the general expectation that the Morrison government is headed for opposition, many people will think (rightly or wrongly) that O'Dwyer was also influenced by the likelihood she faced the grind of opposition, which is a lot less satisfying than the burden of office.

Bad timing for the minister for women

Her insistence at Saturday’s joint news conference with Morrison that he will win the election won’t convince anyone.

If the Liberals didn’t have their acute “woman problem”, O'Dwyer’s jumping ship wouldn’t be such a concern. She’s been a competent minister, not an outstanding performer. She was not in “future leader” lists.

But it’s altogether another matter to have your minister for women bailing out when there has been a huge argument about the dearth of females in Coalition ranks, damaging allegations of bullying within the Liberal party, and high profile Victorian backbencher Julia Banks deserting to the crossbench.

All in all, the Liberal party is presenting a very poor face to women voters. It was O'Dwyer herself who told colleagues last year that the Liberals were widely regarded as “homophobic, anti-women, climate-change deniers”.

Anti-women climate-change deniers?

An effort earlier this month to have assistant ministers Sarah Henderson and Linda Reynolds talk up the Liberals’ credentials on women looked like the gimmick it was.

O'Dwyer says she has “no doubt” her successor as the Higgins candidate will be a woman. Morrison also says he thinks there will be a female replacement.

But this just highlights how the Liberal party’s failure to bring enough women through the ranks now forces it into unfortunate corners.

The candidate will be chosen by a local preselection. As one journalist quipped at the news conference, is the situation that blokes needn’t apply?

And what if a man happened to win? Remember Morrison’s experience in the Wentworth byelection, where he wanted a woman and the preselectors gave him Dave Sharma?

Read more: Grattan on Friday: Wentworth preselectors' rebuff to Morrison caps week of mayhem

Sharma was generally considered a good candidate - and Morrison is happy for him to have his second try against independent Kerryn Phelps at the general election.

Assuming, however, that Higgins preselectors heed the gender call, it seems they will have some strong female contenders to choose from.

Paediatrician Katie Allen, who contested the state election, has flagged she will run; Victorian senator Jane Hume is considering a tilt.

There is inevitable speculation about whether former Abbott chief- of-staff Peta Credlin might chance her arm for preselection.

But her hard-edged political stance would be a risk in an electorate where the Greens have been strong – savvy Liberals point out a climate sceptic wouldn’t play well there. And it would be embarrassing for her if she ran for preselection and was defeated.

O'Dwyer rejects the suggestion she was swayed by the possibility she might lose Higgins. Some Liberals were pessimistic about the seat after the party’s drubbing in the Victorian election, and Labor was ahead in two-party terms in a poll it commissioned late last year.

Read more: Minister for Women Kelly O'Dwyer says Liberals were 'subject to threats' in leadership battle

But the government has a 10% margin in two-party terms against Labor, and despite the polling the ALP doesn’t expect to win the seat. (In 2016 the Greens finished second.)

O'Dwyer, who is also minister for jobs and industrial relations, remains in her positions and in cabinet until the election. Understandably Morrison would not want a reshuffle. But having a lame duck minister in the important IR portfolio is less than optimal.

Attention turns to Bishop

Inevitably O'Dwyer’s announcement has turned attention onto the future of former deputy Liberal leader Julie Bishop. Bishop has said she is contesting the election but there is continuing speculation she might withdraw.

While she has previously left open the possibility of running for the opposition leadership this makes no sense.

Now in her early 60s, her chances of ever becoming PM would be virtually nil if Labor won with a good majority and was set for two terms. That’s if she had the numbers to get the leadership in the first place.

It is assumed Bishop has said she’s staying so she stymies any replacement she doesn’t want (such as attorney-general Christian Porter whose own seat is at risk) and can secure a candidate she favours.

Even though she’s a backbencher now, it would be a another blow for the Liberals if Bishop does decide to retire at the election.

Read more: Julie Bishop goes to backbench, Marise Payne becomes new foreign minister

She was humiliated when she received only a handful of votes in the August leadership ballot. Her treatment left her deeply angry, especially because none of her Western Australian colleagues supported her.

But out in the community she is very popular and many voters still can’t understand why, when there was a change of prime minister, she was not the one chosen.

If Bishop were to walk away, she would be making a rational decision. But it would send another powerful negative vibe to voters about the Liberal party and women.

UPDATE: Jane Hume, interviewed on the ABC on Monday morning, has ruled out running for the Higgins preselection.

UPDATE: In reply to queries to her office, Bishop said on Monday: “I am pre-selected as the member for Curtin and it is my intention to run”.