In some cases, the Round modeling tool does not highlight some of the edges that you would like to round. This can happen because there are gaps. As a consequence, you cannot apply radii to these edges.
To verify the presence of gaps, click the ESC key to close the Round tool and use the Tolerance Check tool (see image below).
In order to solve the problem, the best way is to first verify the geometry and then close the gaps by taking advantage of the ConstructionTree™ structure that will allow you to apply changes to the model and update the geometry.
In some cases, you may also prefer to perform the operation without fixing the geometry.
To do this, choose the Round tool, then select the object. Now, use the CTRL+ENTER shortcut to close the tool without adding radii (They will be added later). Increase the Sew Tolerance as displayed in the image below.
You should increase the Sew Tolerance by small increments until you get the following panel (see image below). This panel informs you that the number of edges has changed. Just click OK.
Now, by using a bigger value for Sew Tolerance (see image below), all the edges are highlighted.
At this point, you can click the Insert Radius checkbox to add the radius you need.
Remember that in order to perform the operation, you will need to apply radii to ALL the edges that had gaps (they were displayed in yellow when you used the Tolerance Check). Of course, you can also add any other radius that you need.