Either one of three is usually occurring:
1. The spring is old/broken that pops up the lid.
2. The lid's hinge is stuck (rare)
3. The release pin is stuck/broken.
To diagnose 3, have one person hold the fuel lid release lever up inside the car. Then attempt to lift the lid. If you are unable to pry it, or risk scratching the car, clean the lid, and use a suction cup to lift it. If it does not lift, then you know that the release pin isn't working. You can remove the release cable from inside the trunk/boot if needed.
Typically, a stuck hinge, or a sticky release pic can be restored with a little silicone crease.
If the spring is broken or loose, you will just have to find a replacement.
The 2001 Mazda MX-5-Miata is a gas-powered vehicle.
The 2002 Mazda MX-5-Miata is a gas-powered vehicle.
The 2009 Mazda MX-5-Miata is a gas-powered vehicle.
The 2006 Mazda MX-5-Miata is a gas-powered vehicle.
The 2004 Mazda MX-5-Miata is a gas-powered vehicle.
The 2012 Mazda MX-5-Miata is a gas-powered vehicle.
The 2013 Mazda MX-5-Miata is a gas-powered vehicle.
The 2003 Mazda MX-5-Miata is a gas-powered vehicle.
The 2011 Mazda MX-5-Miata is a gas-powered vehicle.
The 2007 Mazda MX-5-Miata is a gas-powered vehicle.
The 2005 Mazda MX-5-Miata is a gas-powered vehicle.
The 2008 Mazda MX-5-Miata is a gas-powered vehicle.