@retired?:
How often does a gap cause a problem? If you have one of the best applications in the pool, never - as long as you don't say that the reason for your gap is because you got addicted to Say Yes To The Dress and just stopped going to work. If I have 30 equally qualified candidates and the hiring manager only wants to interview 5, you're out. Same with the guy who lives 6 hours away, and the gal who submitted a resume with a spelling mistake. Obviously, this applies the most to junior positions, since a larger number of the applicants will be equally qualified. Also, if the gap is assumed due to layoffs, it is expected that a petrophysical engineer or a SAP BI functional specialist will take longer to find meaningful employment than a cashier.
How long do you have to work at a firm to be of value? That depends on a lot of things, primarily your industry's culture and your location's culture. As a very general rule I would warn against having any tenure of less than a year unless you work in a very contract-centric industry. Another common assumption (not just made by HR) is that if someone remains in the same role for over 4 years, they are unambitious.
The perception of gaps also vary by the region (the lower the unemployment rate, the more noticeable a gap is) and the nature of your industry. If the job requires ridiculously long hours or extended travel, a gap will be more frowned upon than a job that requires a caring nature and an open-minded worldview.
Good idea to get your resume into the hands of the hiring manager. I would recommend that you still apply through the irritating online tracking system, and then send another copy to the hiring manager with your cover letter directly copied into the body of the email.
(for reference, my industry recruitment experience includes mining, oil & gas, insurance, and 3rd party staffing.)