Exactly the same issue on a Thinkpad X260. This on the latest bios (1.43), freshly patched ACPI files per the guide, properly mapped USB ports and USB power properties and everything else working perfectly.
This appears to be a particular issue with the BCM20703A1 revision. I see on thedarkvoid's repo the latest update to the old BrcmPatchRam notes state 'BCM20703A1 fix'.
I have tried loading various firmwares from .414 all the way up to .481, which I found on a newer driver (latest is .422 on RehabMan's repo). The behaviour is the same: the firmware loads correctly after sleep only on AC power.
On battery, wake results in the device detected as BCM2045A0 and it disconnects when attempting to use it or by itself after a few minutes.
The device only works properly when detected as BCM920703. Why that happens... I have no idea.