I have ran into this a number of times. Just to clear up one thing for those frustrated, just because the error message says it is Connection X doesn't mean it has anything to do with that Connection! The only thing it does seem to tell you that is useful is that it does have to do with the components that Connection X references.
In the case I just figured out Connection 2 was fine but some other component down the structure referenced the part hosting connection 2 as well as another part. EVERY part in a mechanism hopeful assembly needs to have references to only one other part. If you have a part with non-mechanism connections that references two parts it seems to fail one of those parts in mechanism. My guess is the first part in the regen order will have the connection error.
If I can ever figure out how to get the VBAPI to work with Creo maybe I will write a simple script that checks this and notifies you of the perpetrating part. The logic behind this is extremely simple as far as I understand it.
-All parts reference only one other part?
If yes it should work. If not, probably it won't work.
TIP if you are getting that Connection X will be suppressed because of invalid constraints error, zoom out so you can see most of the assembly the error probably resides in, then try to enter into mechanism mode. It gave me an error saying the highlighted constraints are invalid and will be supressed if you continue. You should be able to see highlighted boxes representing each origin of the offending components. You can't zoom or pan (thanks Creo!) so you might have to hit cancel a few times and adjust the zoom then try to enter back into mechanism to see the highlighted boxes.