Fan only works in when high is selected on remote but only runs at medium/slow speed.
Tried new battery.

Does it have pull chain? Check wiring from receiver.
You have Power and they are coded correctly.

I have a hampton bay 52" Ansley with remote control. The fan keeps turning itself off and on. The lighting as well (off and on) all hours of the night and day. The remote operates with 1- 12v battery. It is only 1 year old.

Any solutions?

It does not have a pull chain. The fan was installed by an electrician.

Two reasons that may be happening, may be a third? Remote or remote button malfunctioning, or receiver, receiving signal from nearby transmitter(remote), third would be defective receiver. Pull battery out of your remote, to remove that possibility.

The first poster's problem, the fan has a bad capacitor.

The second poster's problem, she needs to change the frequency of the fan and remote.

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More