FORD SMAX battery problems

[TiffanyP]

Hello 

I have a Ford smax 2010/2011. 
I had a new battery fitted into my car about 6 months a go. In the past month I have had non stop problems with it. 
the radio/sat nav screen stopped coming on and wouldn’t work about 6 weeks ago. It had happened before so I carried on as normal. Then a couple weeks later the car hadn’t been driven in a few days (lockdown etc) and the battery was dead. We charged it up till full. Then it was dead again the next day. 
My husband disconnected the radio/sat nav unit as he thought it was that, that was draining the battery. Charged up again and it was fine for about a week then again today it’s flat and came up engine malfunction. 
 

really frustrating. The radio/sat nav unit is still disconnected and although running fine all week, today it’s not. 
Admittedly I only drive the car short journeys especially at the moment, but normally it’s only really used for school runs and trips the shops. It’s not often driven on a long run. My husband thinks this is the problem but I can’t imagine I’m the only person doing short journeys and have theses problems. 

just to add the starter motor seems to be okay as it starts absolutely fine when it has battery. 
 

any ideas of what I need to do? 
Thanks 

[Meta55]

Think you’ve answered your question. Short journeys in winter can easily kill the battery. Did you buy a decent battery or just go for the cheapest you found. Cheap batteries are cheap for a reason.