Steel rims? You may need to remove the tyres and wire brush the rims to remove the rust where the tyre bead sits. I always insist on doing this when getting tyres fitted. The people in the tyre centre won't like you but tough.
Alloy rims can sometimes go slightly porous with age.
If you like, take the wheels off and hold them in a barrel of water and see if there are any bubbles anywhere. I may just be the valve, or the seal around the valve stem where it goes into the rim, it may be around the beading of the tyre.