Cheap LIFEP04 batteries

[Brissieboy]

You will risk damage to the device/cable/ after 2 to 3 hours because as the battery supply voltage falls the device will draw more current IE as the battery voltage falls the current draw will increase proportionally (P = E x I ... where P equal power, E equals voltage and I equals current).

I disagree with that part. The power delivered will not remain constant so the logic of applying that formula is flawed. As the voltage drops, so will the current supplied, so the power delivered will reduce with the voltage. The possible exception to this would be a brushed motor load which will increase the current draw as its speed reduces and be max when it is stalled, but the voltage would be quite low at this point. And that formula still does not apply.