Quick answer: Use the PlayableGraph play/pause state rather than Stop, and match the director's UpdateMethod to whether you pause with Time.timeScale.
A Timeline that jumps back to the beginning when you unpause was Stopped, not paused. Pausing the playable graph preserves the playhead. Here is how.
How to fix it
1. Pause the graph, do not Stop
Call director.playableGraph.GetRootPlayable(0).SetSpeed(0) to freeze the playhead, then set speed back to 1 to resume. Stop() resets director.time to zero, which is why it restarts.
2. Match the update method to timeScale
If you pause the game with Time.timeScale = 0, set the director's Update Method to GameTime so it freezes too; if it is set to Unscaled Time it keeps running through the pause.
3. Cache and restore time as a fallback
If you must stop, store director.time first, and on resume set the time back and call director.Play() so playback continues from where it left off.
Catching the ones you can't reproduce
The hardest version of this to fix is the one you can't reproduce — it only happens on a player's hardware, OS, driver, or save state, under conditions that simply aren't present on your machine. A report that says “it crashed” or “it froze” gives you nothing to act on, so the bug survives release after release while quietly costing you players.
Automatic error capture closes that gap. Each failure arrives with its full stack trace, the device and OS, the build number, and a breadcrumb trail of what the player did right before it broke, so even a failure you have never seen becomes a specific, reproducible issue. Fold identical failures into one signature ranked by how many players each hits, and your worklist sorts itself worst-first instead of arriving as a stream of vague complaints.
This is where a tool like Bugnet earns its place. Its SDK captures every Unity error automatically with the full stack trace plus device, OS, memory, build, and game-state context, folds duplicates into one grouped issue with an occurrence count, and ties each to the build it first appeared on — so you fix the problem that hurts the most players first and confirm it is gone when its signature disappears from the next release.
Reproduce it once with full context and the fix writes itself. The hunt is the expensive part.