I was 3 cm for a few weeks. Maybe even an entire month. I was also 80% effaced or so around 38 weeks. I was 100% effaced at 39 weeks and he swept my membranes. Daughter was born within 24 hours of that happening. So she was born 2 days before her due date!
Similar story with second daughter; also 3cm for a month, maybe more. Had membranes swept and she was also born 2 days before her due date!
But do know that you can be dilated and effaced for weeks (the effacement is actually what matters more in the early stage. Once you reach 100% you'll really start dilating).