I don't think resoldering it will help. I'm assuming this gas discharge device is to protect the head from static damage when the head is reconnected to the radio. So normally this suppressor is an open circuit and it protects by absorbing, or shorting any static charge to ground, which is the right suppressor lead as shown in your photo. If this has protected the head enough times the gap may be damaged and is shorting out, perhaps a loose speck of metal in the gap randomly shorts it.
If you can tap it with an ohmmeter connected you should see it be either open or shorted as you tap. It has worked as designed so even though it will allow the radio to work if it isn't in the circuit, without it the next static discharge will damage any number of more expensive parts. Well worth replacing it.