You've probably already tried this, but if you are occasionally getting a blip of a signal, the culprit may not be HDCP. I've set up signals from fairly recent Macs via a mini Displayport connection to HDMI, then converted to SDI into a switcher, as well as directly into HDMI recorder that definitely can't record HDCP protected signals. So I'm pretty sure that HDCP is not necessarily always on with Mac laptops.
Does the AJA converter light show that it has locked to a signal? The communication between HDCP requirement mentioned above would not result in a signal lock, as when the mac reads the EDID of the converter, it will simply block out the signal output on the Mac end when displaying HDCP content, as it knows that the converter will send out a non HDCP compliant signal. Similar with a HDMI recorder.
Try different "Sync Speeds" on the Mac, as that could be the issue, especially if you don't have the 3G version of the converter. (I'm guessing you are using the Hi5 line) If I remember correctly from when I worked support for a different company that makes converters, you may need to set it to 30 or 29.97Hz for it to output 59.94, for instance.
It would help to know:
What model mac and how old? If you go to Apple>Get info, you should be able to get the exact model number, usually something like 14,2 or 7,1.
Which version of Mac OS?
What exact model of AJA converter?
What video format are you using on the switcher?
#CrossOver