Conservative current limiting on proper USB host ports (rather than chargers, battery packs and the like) is normal and ordinary, and this is the sort of behaviour I'd expect from a PC (well, I wouldn't expect it to realise what the problem was and notify the user like that, just unceremoniously shut down the port until power-cycled).
Safe, yes. This feature exists to prevent hardware damage. But obviously disks disconnecting at random isn't very good for your data.
Why? Probably one of:
-The disk is playing fast and loose with the USB spec and exceeding the rated current draw.
-The disk has drifted out of spec over time due to a marginal fault (sticky bearings, capacitor rot) and is exceeding the rated current draw.
-TV's 5V power supply isn't quite up to the job and is dropping voltage, triggering this protection.
-Nonspecific gremlins falsely triggering the overcurrent detection.
Further diagnostics: Voltage/current monitoring of the USB power that's fast enough to detect transients. This isn't going to be fun if the fault takes days to recur.
Workaround: Provide the disk with power from an alternative source. Typically, in the absence of provision for such on the drive itself, by inserting a powered USB hub between it and the telly. Might not actually work if the TV's software isn't expecting there to be a hub in the chain. Or you could molish a bodgy splitter cable to bring the 5V supply in from elsewhere while passing through the data..
ETA: Crosspost with Feanor