Intel 7260AC Bluetooth [8087:07dc], Ubuntu, and the Thinkpad T440p
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.