Bird bought a new Mini 3 months ago

Last week the computer dash said she had a flat, went and put some air in (It was only down about 4 on the PSI) and reset the computer

Today its saying its flat again, and it definatly looks to have gone down abit. Havent been to fill it up yet.

Best way of going to get this sorted? Can I just take it to a tyre place and see if its a slow puncture and get it repaired? Or just buy a new tyre? Or do we need to take it to Mini because its connected up to the computer?

Edit - they are runflat tyres aswell

Go to a tire place and let them find the leak. Don't just replace the tire - it might be leaking from the valve stem or because of a seal problem or it may have a repairable puncture. The TPMS and associated onboard monitoring will only be an issue if the sensor (valve stem or seal) is where the leak is.