I'm running marshmallow and I use SIP constantly - is this fixed in CM? Because as far as I know I haven't had any issue here, could just be that my phone doesn't Doze for another reason though.

SIP works, but excepting a native app from Doze doesn’t. For example, if an app has its own push notification system, even if it is whitelisted, it will be terminated during doze.

I'm unable to find any reference to this issue on Google. Is it device or ROM specific perhaps?

Surely another constant connection like SIP would also be terminated, no? I don't see how that would differ from another push notification system.

edit: to be clear I'm using a 3rd party SIP client (Bria), which I have indeed excepted via this method.

No, but this is a bug, confirmed by Dianne Hackborn on G+

Are you referring to https://code.google.com/p/android/issues/detail?id=193802 perhaps?

This was fixed at https://android-review.googlesource.com/#/c/221708/ and probably merged into many custom roms generated since. It also only occurred under fairly specific circumstances.

EDIT: Yup, https://romhut.com/versions/cm-13-0-20160508-v8-0 indicates it's been in CM for a while, which is probably why I haven't experienced it. Dianne Hackborn fixed this as far back as November 2015, it might have made it into 6.0.1 on some devices too, though I could be misreading.

Yup, it got fixed on some devices, but the Nexus 5, for example, never got the fix.

This leads to the problem that you, as a dev, either have to leave a huge amount of users without working push notifications, or use GCM anyway.