Search the Dropbox Watchdog archive
It depends entirely on your plan. Dropbox's own help documentation gives three tiers — 30, 180, or 365 days of file-recovery window depending on your plan — after which deleted files are marked for permanent deletion and can't be recovered. Dropbox's help center doesn't state a retention period for how long personal or team activity-log entries themselves are kept.
Dropbox's version-history overview page states the recovery windows plainly, by plan: "Dropbox Basic, Plus, and Family customers have 30 days. Dropbox Professional, Essentials, Business, and Standard customers have 180 days. Dropbox Business Plus, Advanced, and Enterprise customers have 365 days." Its data-retention help page gives the same structure in slightly different plan groupings: "Dropbox Basic, Plus, and Family customers have 30 days. Dropbox Professional, Standard, Essentials, and Dropbox team users have 180 days. Dropbox Advanced, Enterprise, Education, and Dropbox team Plus users have 365 days."
What happens once that window closes — or once you manually mark a file for permanent deletion — is described the same way on that page: "Dropbox saves deleted and previous versions of files for a specific period of time so you can recover them if desired. After that time, the deleted files are marked for permanent deletion in our system and are removed from our storage servers. Once they've been deleted, they can no longer be recovered or restored." Marking a file for permanent deletion yourself works the same way: "When you mark files for permanent deletion, you initiate the process for permanently deleting your files from our servers. This process can take several days," and again, "You can't recover files once they've been marked for permanent deletion."
Account-level retention is separate from file-level version history. Dropbox's privacy policy states: "When you sign up for an account with us, we'll retain information you store on our Services for as long as your account exists or as long as we need it to provide you the Services. If you delete your account, we'll initiate deletion of this information after 30 days." The policy adds two caveats: "there might be some latency in deleting this information from our servers and back-up storage; and (2) we may retain this information if necessary to comply with our legal obligations, resolve disputes, or enforce our agreements."
Activity logs are a separate question, and Dropbox's help documentation is thinner on it. Its help page on viewing team activity in the admin console explains which actions get logged at all ("Signed in, Linked app for member, and Created shared link" are logged; some actions, like deleted comments, are not) and how quickly an action shows up ("a team member's actions appear in activity logs in a few hours. At most, actions appear within 24 hours") — but nowhere on that page does Dropbox state how long an activity-log entry itself is kept before it ages out. This archive found no Dropbox help page that gives a retention period for activity-log data specifically, as distinct from file version history.
There is also a separate, admin-only 'data retention' feature — Dropbox's Data Governance Add-On — that lets Business-tier admins set custom retention or disposition policies on team folders. That's a paid, team-configured control plane layered on top of the plan-based defaults above; it doesn't change what a Basic, Plus, or Family user should expect for their own deleted files.
This answer is informational, not legal or security advice. Dropbox Watchdog is independent and not affiliated with Dropbox, Inc.