This requires a little magic, unfortunately; either the driver, system, hardware itself, or some combination thereof do not operate well with autosuspend enabled. Disabling autosuspend for this device does appear to resolve dropped / corrupted / weird bluetooth issues.
Based on my googling, I do not believe this to be Thinkpad-specific, rather something the Intel 7260AC firmware isn’t handling properly at the moment. FWIW, I’m running Ubuntu 13.10 (saucy) on the thinkpad in question, and 12.04LTS (precise) on my destop, with the same card sold by Intel in a PCI-e mount.
Based on one posting in particular, the following solution presents itself:
This isn’t ideal — as it should Just Work — but it works, and is certainly less drastic than turning off USB autosuspend globally. In retrospect, having the bluetooth device drop out shortly after boot/resume, but always be available after resuming, was a big clue.