The simple answer is yes.  In fact, many people see a decreased balance with progression of neuropathy.  Although age can also cause some increased instability, peripheral neuropathy can lead to faster progression and poorer balance.  Neuropathy does cause falls and poor balance.

Brandt R Gibson, DPM
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Podiatrist, Neuropathy Doctor, Father of 11 and Founder of Mountain West Foot & Ankle Institute