In my first article addressing neurological symptoms associated with thyroid disease, I talk about treated hypothyroid patients who do not always see complete relief of these type symptoms with hormone replacement therapy.
This was that first article: Thyroid Disease and Peripheral Neuropathy
Following are medical quotes in regard to neuropathy symptoms in thyroid patients and some of this research specifically points out "treated" patients who experience these. Below are some of the quotes and links to medical research.

"Systemic diseases — disorders that affect the entire body —often cause peripheral neuropathy. These disorders may include: Metabolic and endocrine disorders. ...
Hormonal imbalances can disturb normal metabolic processes and cause neuropathies. For example, an underproduction of thyroid hormones slows metabolism, leading to fluid retention and swollen tissues that can exert pressure on peripheral nerves." (National Institute of Neurological Disorders and Stroke)
Link>> Research Article Link

"Thyroid neuropathy
Little is known about thyroid neuropathy, but studies have shown microvascular and endoneurial ischemic involvement like that in diabetes." (Fernando Dangond, MD, Associate Neurologist, Brigham and Women's Hospital; Assistant Professor, Department of Neurology, Harvard Medical School)
Link>> Research Article Link

"The prevalence and characteristics of polyneuropathy were assessed using standard clinical and electrophysiological criteria in 39 consecutive outpatients with primary hypothyroidism, 15 of whom were previously untreated....
Using standard electrophysiological criteria, a definite diagnosis of polyneuropathy was made in 28 cases (72%). The commonest sites of abnormal nerve conduction were the sensory nerves, especially the sural nerve. Polyneuropathy was generally mild." (PubMed)
Link>> Research Article Link

"Conclusions: Some patients treated for hypothyroidism have symptoms and findings compatible with small-fiber neuropathy or "hyperphenomena" indicating central sensitization." (American Academy of Neurology)
Link>> Research Article Link

These research conclusions clearly point out the fact that both untreated and treated hypothyroid patients can potentially experience symptoms of peripheral neuropathy and other neuropathies.