We ran a cheap winch on our old race car trailer. Most of the problems we had with it were nearly always a battery issue. Car batteries used for running a winch often only last 2-3 years. The low voltage in the battery kicks out the resets on the winch motors.

If your winch motor is not getting hot, the problem is likely not a winch problem but a wiring or battery issue. The battery for the remote would be the 1st thing I would replace, if the sensor on the winch isn't getting the signal from the remote, its shutting off. Could be a problem with the receiving sensor as well. Then you need to have the main battery for the winch power load tested, I'm betting it fails that test, even being fully charged.
We got an extra couple years out of marine deep cycle batteries. They were designed to be heavily loaded until nearly dead, then be fully charged, over and over, but that was years ago, might not be the case anymore.