How long does it take to go down?It could be the bead leaking - See the thread below.https://foc-u.co.uk/index.php?topic=26065.0
It might be worth coating the tyre and wheel with a strong solution of water and fairy liquid and wait for a few minutes this usually shows up air leaks. slightly over inflating the tyre can help.Malc
The tyres were on when I bought the bike last year and had a slow puncture nothing drastic but I took it to the local garage to get it sorted. When the guy took the tyre off it was filled with tyre weld so he give it a good clean , changed the valve and checked again for any leaks , everything seemed ok.
Make sure it's Harpic 10x Power Plus. Yeah, use it neat, maybe pour some in an old jar or suitable container and use an old paint brush. Rubber gloves and eyeshields would be a good idea, to be on the safe side.