Same issue here on iOS 27 with a MacBook Air on macOS 27.
iPhone → Mac stops working while Mac → iPhone keeps working. Only restarting the iPhone fixes it; toggling Handoff/Wi-Fi/Bluetooth and a passcode unlock don't. Mac was not restarted.
Console logs from the iPhone while broken show pasted handling the copy normally ("Advertising general pasteboard over Continuity", "Did send update to server"). useractivityd receives it ("[PBOARD CONTROLLER] Got type update from client"), but then never schedules updateAdvertisedItems, so the clipboard is never added to the Bluetooth advertisement (no pb-1 / UAPasteboardAvailable). While working, the re-check follows within milliseconds.
Filed as FB24924733 with sysdiagnose and captures.