According to the BLS (which is the data they cite), the unemployment rates are [1]:
Women
25-54: 5.3%
50-54: 4.4%
55-59: 4.2%
60-64: 4.1%
65+ : 4.7%
Men
25-54: 5.2%
50-54: 4.3%
55-59: 4.4%
60-64: 4.6%
65+ : 4.6%
There doesn't seem to be much difference in the overall unemployment rate. However, maybe the unemployment is cycling between many different men for shorter periods of time. If women who were employed kept their jobs, it could lead to a stable set of women who are employed while the unemployed women are unemployed for longer - which is worse for those unemployed individuals than having the same number unemployed, but that unemployment cycling between individuals. For example, if we have 10 people and 2 are going to be unemployed, if Sara and Josh are just always unemployed, it sucks to be Sara or Josh. If everyone takes their turn and is unemployed 20% of the time, that sucks for everyone, but sucks substantially less.
But looking at the BLS long term unemployment statistics, that doesn't seem to be indicated more for women than men [2]. Looking at the rise in long term unemployment from 2008-2013:
Women
45-54: 222% (of 2008 long-term unemployment)
55-64: 284%
Men
45-54: 218%
55-64: 341%
It seems like the number of long-term unemployed has increased around the same over the period used by the article regardless of gender.
But what if the labor force participation rate dropped hugely for women and so they're not showing up as long-term unemployed since they aren't considered part of the labor force anymore? http://www.bls.gov/emp/ep_table_303.htm
I'm not going to copy all the data in from that link, but women 55+ increased participation by 14.4% from 2004-2014 while men 55+ increased participation by 6.25%. That's not something I want to draw a great conclusion from since women born closer to the present are more likely to have jobs than women born farther in the past (ie. a 55 year old in 2014 is more likely to have had a career than a 55 year old in 2004 because the past sucked and whatnot). Given that men 25-54 decreased participation by 2.5% while women 25-54 decreased participation by 1.9%, I think it's fair to say that the 14.4% increase isn't just due to more women 10 years ahead in time having careers.
I have to say, this just looks like shoddy reporting. Based on the numbers, the article seems more clickbait than reporting. It's crappy that some people who are skilled are having trouble finding jobs. We're talking about people's lives here and it sucks to be out of a livelihood. But the thesis of the article - that women over 50 are specifically having a problem - doesn't seem to be borne out by the numbers that they in fact cite. The numbers do show long term unemployment up for those over 50, but even there it's up similar amounts overall (total long-term unemployment for those 16 and over is 245% of 2008 levels). Eye-balling it, it doesn't look like there's a spared group besides 16-19 year olds.
Am I hugely missing something?
[1] http://www.bls.gov/cps/cpsaat03.pdf
[2] http://www.bls.gov/bls/cps_fact_sheets/ltu_mock.htm