GFI frequently tripping
It's true GFCI's do go bad and will wear out over multiple trips. So replacing one after 30 years is a good idea since the replacement is not all that expensive. But lets say the replacement does not fix the problem. 

So to start, let's look at how a GFCI works. It is a closed loop system unlike an overcurrent protection. It actually measures the current in the hot wire against the return current in the neutral and if it senses a slight difference. It acknowledges there is leakage in the circuit itself. Since it is not intelligent it can only assume that there is a problem and therefore it trips. 

When we troubleshoot a GFCI. WE start by removing all loads attached to the device. Then if we reset the device and check to see if trips. If it does not trip then one or more of the pieces of equipment attached to the circuit has some sort of problem. If it does trip we know that the installed GFCI device and its circuit is the problem and you begin a step by step approach to investigate and locate the problem internal to the circuit itself.

Moisture is a big player in GFCI tripping and you don't need much. For example many times on a construction site after a rain, an extension cord with a very small crack or cut in the jacket, not the insulation, will absorb enough moisture into the fill material of the cord to trip a GFCI. Remove the cord and set it out in the sun to dry for a few hours and you will be able to plug it back in and it will work.

So remove all equipment from the circuit. Check all cordage and exterior devices for moisture and make sure they are in good condition, clean and dry. Pay attention to equipment cordage that is making contact with the earth. More than likely the problem will make itself apparent. Reset the GFCI, if it stays reset then plug each piece of equipment onto the circuit one at a time and check to see which pieces of equipment are tripped your device. Replace or repair any piece of equipment causing a trip. 

Hope this helps.