Im guessing that you didnt have a shut in royalty or depth clause? Before the production language of 90 days there is likely a statement, I’m paraphrasing here, “that the Lessee shall pay a royalty of $1.00 per net acre, per year on the anniversary of the lease, when payment is made, its considered gas and oil are being produced”. Theres not much you can do unless they dont make the payment on the “anniversary day” of your lease.
The question is whether there were operations, such as repairs or workover, on the well during the 90-day period when the well did not produce. If production was reestablished at the end of 90 days, there is a good likelihood that the operator was actively doing something out there. If there is still no production, then you could send a certified letter to the oil company noting that there has been no production for over 90 days and that your lease provides that it expires after a cessation of production for 60 days and so the lease may have expired. Do not claim that the lease has actually expired. Ask for detailed information about the operations on the well since the well ceased producing, including copies of service records and the dates of those activities. This can be tricky so if you do not have experience, you should have an oil and gas attorney help you with this letter. Also, the attorney can review the lease and make sure that there is not other language which would override the 60 day period.