Perhaps the issue is not because of the router generating the signal. Instead, perhaps the issue is due to a source of noise/interference? So when you walk away from the router, there is still perfectly good signal there, but your device is overwhelmed by noise nearby?
I'd suggest using a hand-held wifi checker and look for congestion etc. too, but if there is random noise (i.e., *not* official wifi channels) then your wifi checker may not help identify if it even exists (like a noisy microwave oven or wireless phone, or some industrial thing you can't control). Are you in a congested area, maybe a wifi checker will show there are tons of channels you are competing with?