Your question is one of "contract law". In contracts, everything is legal where the two parties entering into the contract have a "meeting of the minds." If there is not a meeting of the minds then there is no contract and a court would likely void the agreement. However, for some terms courts will sometimes imply a missing/vague term if there is an easy way to do so. Contract duration is one of those terms that may be "filled in."

First, you must look to the "4 corners" of the contract. This means you don't look to any of the web pages except the agreement itself. Help zones and other pages do not get considered. For websites, the contract is usually the "license agreement" where the user clicks "I agree" during the payment process. If it does not state the term there, the courts will consider evidence of similar web sites to see if they use a 30 day rule.

Also, the amount you're disputing is likely 1 day and unless the membership is extremely expensive you aren't really going to incur the expenses of going to court to recover that money.

As on a side note, if the website deals with any illegal matter such as illegal gambling, illegal pornography, etc. the courts will not find a valid contract and will also not force the illegal website owner to return any money.

When a court must interpret a contract, it gives words their ordinary, everyday meanings unless the parties have expressly agreed that particular words mean something else. If a contract uses the word "month" without providing an alternate definition, courts will interpret the word the way everybody else does -- as a calendar month.

In practical terms,billing in 30-day increments rather than monthly doesn't make much sense. Clients who are accustomed to paying their other bills once a month will not like this company's idiosyncratic schedule and they take their business elsewhere for the sake of convenience.

If the company wants to charge clients for 30-day increments, it should say so expressly in its contract. Inserting such language in the middle of a long boilerplate agreement briefly displayed on a computer screen -- presumably in the hope that most users won't see it -- would be dishonest. Courts will not look kindly upon such behavior.

My sense is that the company is trying to mislead customers so that they will sometimes pay late, perhaps incurring a penalty as a result. That would amount to fraud and could have very serious legal consequences.