UPDATE (2021/05/19): For all of my cancelled flights (over 100) I have - based on my choice - either received full reimbursement or was able to re-book into the future. The refunds office is pretty much back on track again to quickly refund your cancelled flights. Top notch service by Swiss!
Being a HON Circle member, I can tell you first-hand that out of my already 80+ cancelled flights since March 19, 2020 at the time of this writing, not a single leg of the ones I did not post-pone has been refunded.
The reason you are waiting: for the first couple of months the refund office was closed down due to Covid-19. They have only recently begun to process the huge backlog of refunds and are ramping up as quickly as possible.
Plea for more information: you didn't specify your fare class, origin, destination, date of purchase, origin of purchase (LX site, third-party vendor), method of purchase, etc. Therefore, it's difficult to gauge which process your refund will take.
Answering your question: complaints can be initiated through here: https://www.swiss.com/ch/EN/customer-support/complaints-and-compliments. It will go to even a larger queue of pending requests than your refund inquiry. Once you share more information, maybe there is another way.
Two options for you going forward:
- Patience on your side given what you have just learned.
- Complain (does not speed up the other queue given these challenging times)