It depends on who refurbished it. My refurbished Note 3 still works after about 4years - it was refurbished by AT&T.
Sometimes, "refurbished" means that someone bought it, didn't like it after a few days, and got a different phone, and there were never any problems with it. Other times it can be as bad as water damage that was never fixed (it doesn't pay - eventually the motherboard will rot) - Mooncatt's experience. (And that's iPhones, in the case of one repair shop owner who posts to YouTube - you wouldn't believe the "refurbs" she shows - directly from Apple.)
I've also bought refurbs from resellers - and returned them because they had problems. If at all possible, I'd suggest staying away from a refurb.