If you use a capture device in Resolume, it can only have a single specific stream setting in all the clip in stances.
For example, if you want to capture 720p, and 1080p, or different inputs in the same deck, that won't be possible.
But if you don't change signals, having multiple instances of the same input should be no problem. You can then use the clip transform for example to scale and reposition the image.
If you need to switch cables, I'd recommend a switcher which can output to a specific format, instead of cable pulling. That will be a lot more stable on the long run, and doesn't confuse drivers either.
So, what did change on the machine when the card stopped working?
Did it stop mid session, or after a program or driver update?