I don't use my ride on lawnmower all winter (like most of us) the batteries are expensive and I want to look after it - and my question is - do I charge the battery every (say) month or so to keep it charged or do I let it go completely flat and charge it when I need to use the mower again? My battery is a Y60-N24AL-B - 12 volts - 6amp - 12.5 ah. Thanks.

I'd put a Float charger... not a trickle charger (they are NOT the same) on it all winter. They don't cost that much and it will maximise battery life.

Letting it go completely flat will 100% guarantee you will be buying another one very soon... and frequently. These are NOT deep discharge batteries. Full discharge is a kiss of death on a lead acid battery.

Personally, I would try to find an alternate attachment method than the clips that's less likely to short against the frame. A charger such as this would do. Grip 38020 12V Automatic Battery Float Charger

Expect to replace the battery every 5 years regardless.