Hi,
We may be looking at two issue running together.
It is possible that the Mac can get locked out of the iMessages servers for no apparent reason.
Basically this from the start of OS X 10.8.2 shows that this is possible:-
This is what happens when the Serial Number is missing.
We know that there are at least two types of "Silent" failures (before the Yosemite SMS link ability) which showed up as All contacts going red and "not Registered with iMessages" alerts being shown. The other is when sending a iMessage always gets a "Not Delivered" alert appearing under the text.
Both these mean you are not logged in (? fully) from the Mac for iMessages - the presumption being you can use the same ID to login to other services (different Servers) and even with different devices to the iMessages servers.
However at the same time the iPhone has to have the same Apple ID in use to work over your Local network for the SMS to be forwarded to the Mac from the iPhone's carrier service.
This works as the iPhone and Mac are linked locally and not just with the iMessages servers.
Ergo the SMS function may keep working even though the Mac does not has full login with the iMessages servers.
It used to be that we suggested phoning Apple Support, saying you had a login /Apple ID issue (free to fix) and got (asked for ) a level 2 person and got them to look a the iMessages servers regarding your Mac login and they would reset it.
Then the issue seemed to be more common and also further away in time from the Pic above error.
This seemed to cause a moment towards the Engineers being involved and lots of testing and the Level 2s not solving the issue on their own.
If it is the Mac's use to the Apple ID used for iMessages only a reset seems to fix it.
The Serial Number is used for two reasons.
1) A unique login for each device.
2) a security feature that stops a Man-in-the-Middle attacks (people pretending to be your Mac)
Obviously it seems to be being triggered by ordinary events and causing everyone a headache.
Apple are obviously looking for this cause rather then endlessly resetting everyone that phones up.
9:28 p.m. Saturday; August 1, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad