Tasks I add get deleted after some time when syncing with iCloud CalDAV

Usually this is a stale sync state between devices. Keep in mind that Apple's Reminders app does not share its lists through iCloud CalDAV at all — a list that only exists inside Reminders cannot sync through iCloud CalDAV.

If you want your tasks to keep living inside Apple's Reminders app, switch 2Do to its dedicated Apple Reminders sync method (native EventKit) instead of iCloud CalDAV — it's a separate account type that talks to Reminders directly. If you'd rather not depend on Reminders at all, Dropbox sync carries the most 2Do detail.

See Reminders and iCloud CalDAV for the background and recovery steps.