Yes, a contract implied in fact can supersede a written contract: if it both (1) arises after the parties have entered into their initial agreement and (2) if the subject matter of the agreement is not subject to the statutes of frauds (i.e. to a statutory requirement that agreements of this kind must always be in writing).
A course of dealings before a written contract is signed if the contract states that it is the entire agreement of the parties, or appears from context to be the entire agreement of the parties, may not be considered pursuant to something known as the parole evidence rule (which is actually a rule of substantive law and not evidence, despite the name).
An agreement that is required by statute to be modified in writing, something called a statute of frauds, might or might not be susceptible to being modified in this way. Sometimes, failure to comply with a statute of frauds is excused if the parties have partially performed the unwritten agreement, sometimes the statute is applied more strictly and cannot be overcome.
Indeed, in Colorado, where I practice law most of the time, there is actually case law that specifically provides that even if a written contract states that it may only be modified in writing, that any oral or implied in fact agreement which could form a contract in the first place may supersede the written agreement.
Proving that the course of dealings actually constituted an actual modification of the contractual obligation, may, in practice, be a challenging matter, however.
In practice, there is probably a stronger argument on the available facts in the question, that there has been a waiver of the requirement for further provision of the service that may not be undone retroactively, but may be reasserted prospectively with fair notice to the other party, with the written contract remaining in force.
The judge or jury would have to listen to the facts from the parties about their course of dealings and communications, about the nature of the "requirement", and about the pertinent terms of the written contract, and more generally, the larger context of the transaction, and then would decide which interpretation seemed closer to the truth, or if another explanation of what happened was more plausible.
This dilemma and uncertainty is generically a problem any time that the parties course of dealings deviates significantly from a written instrument. These kinds of cases are never clear slam dunks for either party in the event of litigation.