Why did I lose my conversation history on desktop?

Data storage when using Wire on the Web and Desktop is based on IndexedDB, which is managed by the browser (Google Chrome, Firefox). When storage on the local machine is running low (“under storage pressure”), user agents automatically clear storage to make more available space. This can also affect the data storage of Wire. Therefore, it is important to have enough free storage of the device (min. 20% free disk space available).

See: https://developers.google.com/web/updates/2016/06/persistent-storage

Upcoming versions of Wire will use a different database schema, that is no longer affected by this behaviour.