Mix you up some soapy water and put around the tire, (tyre) and see if it is leaking around the tire bead. If it is you will probably have problems with the new tires also. Like I had mentioned before the chrome gets very small cracks and the air escapes very slowly. Ford actually had a recall on the 2005 Thunderbird I believe because of the tiny cracks in the plating on the factory installed wheels. I guess you could go around the wheel and find where the leak is and mark it and when you pull the tire off see if you can see the place and maybe grind the chrome off to stop the leak.
This is another reason I do not like chrome wheels. Aluminum has no plating and holds better. You could always go to a tube but radial tires do not like tubes and require a special one due to all the sidewall movement.
This is a link that discusses the issue and their Discount tire dealer says they see it every day. Very prevalent in Chrysler & Lexus wheels.
https://www.truedelta.com/pieces/chromewheels.php
Here is another link that talks about the issue and their solutions. I see they recommend that you use the dry nitrogen to fill any alloy wheel so there is not moisture to start the corrosion.
http://www.thewheelwarehouse.com/services/corrosion-and-leak-repair/
Ford's solution on some wheels like my 2002 F-150 was to use steel wheels and then glue a chrome plated plastic cover onto the steel wheel. The tire is seated on the steel wheel and the chrome is like a permanent wheel cover. They do not leak.
If it is leaking around the tire fill valve you can have them put some RTV around it after cleaning and might help. Some people actually put sealer around the tire bead also. Chrome wheels are a PIA in my opinion. I have Magnum 500 wheels on one of my cars and will probably pull off due to leaks.
Another situation where we had leaks through the cracks in chrome was on Nitrogen filled Die Springs used in Automotive stamping dies. The nitrogen would slowly leak out we would rebuild the cylinders with all new seals and still leak. It turned out when they viewed the chrome under electron microscope they could see the tiny cracks and changed their plating process to fix the issue. Those cylinders have thousands of pounds of pressure in them.