To be deductible, a business expense must be both ordinary and necessary. An ordinary expense is one that is common and accepted in your trade or business. A necessary expense is one that is helpful and appropriate for your trade or business. An expense does not have to be indispensable to be considered necessary.
So the first question the IRS agent would ask if you deduct gym membership fees - is that business expense expense ordinary (common and accepted in your trade or business) AND necessary (helpful and appropriate for your trade or business).
I assume the answer will be negative...
IRS specifically list among Expenses You Cannot Deduct - see page 39
-- Dues to business, social, athletic, luncheon, sporting, airline, and hotel clubs.
To be precised - these fees might be deductible - but that is based on the type of your trade or business - for instance if you are a professional athlete - such fees might be viewed as both ordinary and necessary.
However - for most types of business - that is personal nondeductible expense.
Sorry if you expected differently.