Please note: the feature will become unavailable in Chrome 85 after Wednesday September 30th. It will be available again in Chrome 86+, due for release next week.
The underlying feature in Chrome for file system access was previously in an experimental state, and the experiment is ending on September 30th, making the feature unavailable in Chrome 85. The reason the experiment is ending is because it is now enabled by default and available to all websites in Chrome 86+, which is scheduled for release on October 6th. This means there's an approximately one week gap in between where the feature will be disabled in the latest Chrome release.
The one-week gap is actually an intentional part of the way Chrome handles experimental features. It is designed to ensure websites using the feature rely on detecting the availability of the feature rather than a specific browser, since relying on browser detection has been a long-standing compatibility problem for the web. (Construct of course already relies on feature detection, which it uses to decide whether or not to show the save options - which is why you may see them disappear.)
As I've previously noted, experimental features are subject to change at any time. (I've also updated the editor for future releases to more clearly state that experimental features are subject to change at any time). If you need to use the feature during the intervening week I would advise to use Chrome Beta, which is already on version 86 and therefore has the feature enabled. Alternatively you can temporarily go back to using the other save options like Cloud Save. Once everyone is on Chrome 86+ in a few weeks, the feature will have fully graduated to a widespread stable release, so there should be no further such interruptions to the availability of local file/folder save options in future.