In general, the number of employees working flexibly at their own request usually stalls or declines in a recession, not only because employers cut back but because employees fear straying from the norm. The number of corporate telecommuters edged lower in the 2001 recession, then recovered, only to decline to 8.7 million in 2009 from 9.2 million in 2006, says Ray Boggs of IDC, a Framingham, Mass., research concern.

Some managers harbor stereotypes that people who work part-time or take leaves lack commitment. Amid rising discrimination complaints to the Equal Employment Opportunity Commission, the agency is holding a hearing Wednesday on bias against people with caregiving duties.

To improve your survival chances, ask yourself, 'What's most important to my company right now, and how do I make sure I'm contributing to that, and that my achievement is visible to my boss?' says Sarah Grayson, a partner in On-Ramps, a New York search firm.

'If you're doing something peripheral, figure out how to get involved with something that is not,' says Liz Polk Lynch, a San Francisco group manager for a software firm. At her company, 'I've never had anyone come to me and say, 'So-and-so doesn't work Fridays, so can we let them go?'' says Ms. Lynch. 'I hear, 'So-and-so's job performance seems to be slipping, or they don't seem to be working on critical projects, so can we let them go?''

Make sure your goals are clear and your output first-rate. Establish 'an ongoing conversation' with your boss, says Cali Williams Yost, a Madison, N.J., consultant. 'Sit down, talk about how it's working.'

Be willing to bend a bit -- even though it forces work-life sacrifices. Part-timer Anne Abreu, a San Mateo, Calif., insurance specialist, knows her schedule puts her 'under the spotlight,' she says. So she is often at the office on her day off to work or attend meetings. In a nontraditional setup, she says, 'you need to be realistic, be flexible and deliver results.'