I have two objects and a connector between them. All is ok, but when I add one of the objects to some group, the connector stops working - if I move the group or the other object the connector doesn't follow

The grouping takes the grouped objects to a new level (in the XML), and thereby 'out of sight' of the connector (whyever). You might use layers to separate different groups of objects, connectors will work between layers. Or you re-select the objects you would like to move simultaneously with Shift-click everytime, which might be a pain.
DeGrouping after movement of the group will let the connector snap back to its original target, too,so that might be a workaround; sadly the 'undo: ungroup' undoes the snapping too....
Weird Trick: If you have objects A,B and C, try connect A and B, then group B and C -> Problem. But: additionally 'group' just A(no visible effects, just the XML code gets another group object containing just one object), then 'ungroup' A, and the connector snaps to the right position.
Bug or Feature? the eternal question...