No access to region?

Solution 1:

The road advisor deeply cares that all of your buildings be attached to the region. If any buildings are not connected, he will complain that there is no region access. In the above picture, I have demolished some roads and some decorative cinderblocks are left behind. Since this former decorative part of an industrial zone has no road, it has no region access.

If you hover over the little triangle by the advisor's head, then click on the little red road icon, you can cycle through the occurrences of such buildings. This works for fires, crimes and abandoned buildings as well, from their advisors.

I have tried to connect my cinderblocks to a road, but the roads do not cooperate. As a decorative building, it's immune to direct bulldozing. I just let the road advisor worry about it.

Solution 2:

No, heavy traffic cannot disconnect your city from the region. At least not literally. Traffic can affect all vehicle agents coming in and out, but it cannot actually sever your connection to the region.

While I was learning the game, I had a 4 way intersection very close to the highway, and was able to build up traffic gridlock all the way up the regional highway without getting any sort of error about disconnection.

In your case here, it looks like something funky might be going on with the avenue in front of the skyscraper to the far right. You can see the driveway for the building coming off of there, and it looks like your streetcar rails are caving inward around this. I would demo that intersection and see if you can get things together again while paused. Even if you accidentally knockdown that skyscraper, it will quickly rebuild itself.