This has happened to me many times as well, even on standard FireWire captures. I stopped using the capture feature in Premiere Pro and used other tools. For FireWire captures i used ScenalyzerLive and never lost a capture.
For Blackmagic Design cards, use Blackmagic Design Media Express that you already have installed. You won´t regret ditching the capture feature in Premiere Pro.
Tried it today seems ok can't quite work out how to save the capture yet!!!
There was some time ago i used Blackmagic Design Media Express but if i remember correctly the file is continuously written to disk while capturing meaning that when done capturing the file is already by default saved to disc. So there is nothing to save since the file has already been written to disk and that´s the biggest difference between Premiere Pro and other capture apps.
To find the file/s:
In Blackmagic Design Media Express, go to Edit > Preferences and look for "Capture audio and video to:". In the folder you find there is where your files are and they can be found with any file explorer. You can change that file path as well to a folder that may be better/more preferred than to capturing to the system disk.
I contacted Adobe and they tell me there is a known bug in Premiere Pro but do not know when/if it will solved.
Looks like I will have to switch to Blackmagic software which I'm told is a very good program and of course you only buy it outright ONCE. Or use the FREE version whioch is hardly any different. Then I can stop paying this high monthly fee.