How long can open angle glaucoma go untreated?

Never good. Unfortunately, undiagnosed glaucomatous disease & failure to adhere to recommended prescribed treatments for those diagnosed are two of the biggest issues of managing an otherwise very treatable & stabilizable Disease. The best advice is to have a comprehensive eye exam before age 40, particularly if you are in a a high risk group. .
Short time. We need to differentiate between narrow angles, which is a discriptive anatomic condition, where the anterior chamber angle is narrow, and a narrow angle attack, which is an acute elevation of pressure caused by closure of the angle, blocking fluid flow and causing an acute elevation of pressure. There is also a condition called chronic narrow angle where there are intermittant bouts of pressure.