Hi Alex,
I assume that you are using Custom grids. The labels are determined by the intersection of the features you are using for the grid with the edges of the map frame. If a feature intersects the map frame multiple times you will get multiple labels.
Currently, the dynamic visibility of these labels can only be controlled for each edge. This may be useful if your map is rotated. If not, then the only other option is to convert the grid to either graphics or to features and manually remove the duplicates. No an ideal solution, but a workaround.
I'm not aware of any enhancement request for this or a post on ArcGIS Ideas. Please feel free to post a request for this enhancement there if you like.
Thanks for the feedback.
Tom