Are you saying that you went through the entire Zero Setting procedure, and it was working fine in all gears, and then the issue was happening?
On the power unit, a green light means the rear derailleur.
Strictly speaking the green LED on the PU has two functions.
On switch on, it should flash green briefly - this confirms sufficient charge in the battery to run at the very least, the diagnostics.
In diagnostics, the green LED lighting plus the buzzer may indicate a rear-derailleur *related* problem - it is not necessarily an indicator of a problem of the RD. It might be indicationg a poor (dirty, oxidised, water present) connection the the RD, it might be indicating a problem inside the RD (most often the position resolver not functioning correctly) or it might be indicating an error in the software that controls the RD, within the PU.
In the event of a "one off" occurrence of the green LED / buzzer, either mode button can be short-pressed - if the cause is amomentary "glitch" in the software, a short press of either mode button should restore normal function.
If a reperat occurrence - then careful check should be made of the cable from the PU to the connector, and from the connector to the RD for damage - this can occur from snagging inside the frame, abrasion at the entry / exit ports or by the BB axle, of from some other type of mechanical interference with the cable.
If a check on the cable shows no abnormality, check inside the plug connection for oxidisation, dirt, grease or water.
If both these checks prove negative, then return of the RD to a Service Centre via your retailer is the best course of action. The SC can evaluate the RD on a standard system and will repair or replace as required.
To correct / expand an earlier post, "early production was not the best" There was a specific issue with a percentage of early production v1 PUs in Record and Super Record - the very first production in late 2011, early 2012 was fine, there was then a short period where a production change was made which caused a problem (unfortunately this took a few months "in the wild" to manifest itself, testing had not revealed it as an issue) ... this change was reversed in early summer 2012 and subsequent production (including all Athena v1) was essentially problem-free.
There have been issues not related to manufacture but to storage of PUs that have started to manifest themselves recently - PUs, v1 particularly (these having been in storage longest) have not been regularly recharged in storage, leading to a well-known and understood problem that all Lithium Ion batteries can suffer from - under-volting. Users should be advised that under-volting is not a Campagnolo warranty issue - it is down to the distribution network and then to the final user, to ensure correct storage of PUs and Campagnolo do not warranty for this issue.