UPDATED FOR TAX YEAR 2019
Yes - it is considered a medical expense as long as you get some medical services for the fee.
The IRS says retainers may be deductible -- or a legitimate expense for a health savings account -- depending on what you get for your money. If your fee pays for you to get a physical once or twice a year, plus ready access in emergencies, then you're paying for deductible services and the retainer is also deductible.
If all you get is access, and the fee doesn't pay for any services, you won't be able to take the deduction. If part of the fee is for services, that part is deductible.
[Edited | 4/6/2020 | 11:32am PDT]
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