My 1996 Chevrolet Corvette has a slow leak

I’ve taken it to the tire shops and they cannot locate a leak, but if I leave the car in my garage a week it goes flat. What can I do to try and fing this leak.

The usual check is to put the wheel in a water bath deep enough to cover it and hold it down until you can see the bubble where the air is coming out. The shops may be using a soap mix which in my experience. is no as sensitive. If you have alloy wheels it may be the wheel that is leaking so don’t miss looking there. It may also be a situation where it only leaks when it is under load.

One possible idea would be to switch tyres on the same axel so the tyre is no longer on the same rim.  If the leak disappears. it was likely the seal between the rim and the tyre, if it follows the tyre, you know what tyre it is or if it follows the rim, you know it is rim related (porous or corroded or damaged rim) 

Good Luck

One Thing You Can Try At Home:

Spray some window cleaner or soapy spray on and around the valve stem. Wiggle the stem a bit and see if bubbles of cleaner form from leaking air. There are a lot of bad stems out there and even a recall.

There are a lot of bad stems out there and even a recall.

Definitely. One of my cars had a bad batch from when I bought new tires a couple of years ago. These were apparently part of the recall, all originating from a certain overseas supplier. After about 2 years, they tend to crack near the base.

This past November, the stem began leaking while my wife and I were driving on the interstate. The tire went flat in seconds. It was very scary.

I’m not saying the OP has a bad valve stem, but to anyone reading this, please check your valve stems! Lean the valve slightly and look for cracks near the base. If you see any cracking, replace the valve.

It sounds to me like you need to find a better tire shop. It should not be that hard to find. I have dealt with leaks that were slower than yours.