Early ZETA Jazz bridges use the strings to pass the ground (coming from the tailpiece) to the pickup elements in the bridge. Most 'sound' issues related to an individual string arise from an intermittent ground problem. To check for a grounding issue simply touch a working string to the problem string using a penny or a paper clip (behind the bridge). If the sound of the problem string comes back then you can assume the problem string has lost its ground.
A signal element (single string pickup) ground can be lost for a couple reasons . . . a bad string for instance . . . but typically it is the string to tailpiece connection. Most often the strings fine tuner is the issue. Sometimes ground is lost when the fine tuner is turned in excessively (down to far). When this is the case, the fine point of the adjustment screw has lost its contact with the pivoting piece of the fine tuner and consequently its ground connection with the body of the tailpiece . . . so start by detuning the fine tuner. In some cases simple corrosion has broken the ground connection indicating a good cleaning is in order, and possibly a little filing or scraping of the corroded surface in question.
If 'grounding' the string does not fix the sound problem, then the pickup element itself may be the cause. Problems at the element could be a broken signal wire or solder joint . . . or a short between the ground and signal. Beyond this the preamp would be suspect. Repairs involving any of these issues would be best resolved at our ZETA shop. Simply fill out our 'Repairs' form (here) describing the problem in detail. Be sure to include your phone number and full address (for return of your instrument to you) and ship your instrument to us at the ZETA shop address.
If shipping from overseas be sure to document your shipment as an item being sent for repair.