By package or cartridge, I consider 4-6 months insane.
As it is, cartridge blades may be sharp for a while, but the roughened edge will be tearing up your face long before the edge won't cut hair. The best blades might hold up to 14 uses at best before they are raking up your skin.
Another reason this claim of 4-6 months is so suspect is that the blades become clogged to the point they can't be cleaned well enough to avoid a rough shave. Sometimes even a toothbrush scrubbing won't clear out all the whisker debris.
So while the blade may be sharp enough to cut to skin after 4-6 months, the edge will be so rough and the cartridge so clogged, it would feel like shaving with sandpaper after a couple of weeks.
And like yourself, most men notice a distinctly uncomfortable shave about 3-5 uses out of the package.
Brushless or lather, boys, which ever you've the notion,
fifty cents for shaving cream, a dollar for the lotion; "Old Spice is quality," said the Captain to the Bosun, "so look for the bottle with the ship that sails the ocean!"