Are you having a problem when not using the adapter? If your problem happens all the time then it's time for a new cable. If it only happens with the adapter then you should consider a new adapter, or a new cable with the proper termination.
For replacement cables you are stuck with purchasing a replacement from Sennheiser, or buying an upgrade cable from Soloz Audio. Those are the only places to get HD555/HD595 cables. The good news is that the cable has a connector and is easily replacable. You don't have to solder or have any special tools other than a small philips screwdriver.
I'm 95% sure it's the adapter because the first one I got had this problem really bad to the point where I would get maybe 1 hour of use then it would crap out. With this connector I only had the problem once when I dropped my headphones (and tugged the cable, I think).
If I try to immediately reconnect I still don't get stereo, which makes me believe it's a software issue too. The day after I dropped my headphones I used my laptop without them, turned off and when I went back home they were working fine.
Shouldn't any audio cable work with any headphones as long as you can wire them correctly? I could look around for an audio store to replace the cable for me here. I remember seeing a street with lots of audio equipment and I'm sure they wouldn't mind exchanging the cable for me as long as any cable works.