This has been glitchy for years. Like some PPs mentioned, switch browsers eg try chrome or firefox. Try incognito.
Also load the hard to get ADRs on the last few days of your trip with the less in demand restaurants at the beginning of your vacation. Give the high demand restaurants a few extra days +60 days to make it a bit easier to get that reservation. eg prioritize Story Book Dining, BOG and Homecomin' as the first ADRs you make right when the booking window opens and book for the last 2 or 3 nights of your trip. Work backward booking your ADRs last night to first. Keep in mind your park reservations and where you will be each day.