It sounds more like voltage regulator is faulty and/or wiring harness/connectors.
The units are small and do overheat but in my experience, 'customers' compounded or caused quite a few problems.
The cdi units have to pass about 4 amps to/from coils (forget which, haven't looked at CB650 since 1980 and CB750/900 DOHC since 1986~87)
Mounting them on a heat sink may help.
The other problem may be not switching ignition off or faulty switch, ( I've seen it happen where people fill up a gas station, hit kill switch then switch it back to ON while filling up, part of reason Honda used keyed caps, have to switch off ignition when filling)
current is flowing through coils and 'boxes' when its switched on, relying on pulses switching off to prevent overheating (if you leave ignition on for 20~30 mins without engine running, the potting compound will show which bits overheated inside, usually they are visible from outside
)
Just my thoughts,
PJ