Lightroom stores the values to a higher precision than displayed but it appears to round them for the formatted presentation in the metadata panel. I'm not sure how you can get the higher precision values out without a plugin (which is how I got them out to check). There doesn't seem to be any inbuilt format for the higher precision values but someone may correct me on that. I have had no problems locating photos a lot closer than a second of arc apart...
Do they appear correctly in the map view? If not then it maybe associated with the input. Certainly pegging them with the mouse works fine.
Many people have asked for GPS coordinates to be displayed with higher precision. Please add your vote and opinion to this feature request in the official Adobe feedback forum: Lightroom: Display GPS coordinates with more precision. That will make it a little more likely that Adobe might respond. The more details you provide, the more likely you'll have influence.
Meanwhile, the Geoencoding Support plugin will display the coordinates with much more precision (millionths of a degree, or about 4/1000 of a second). That plugin is in general much more capable than the builtin geo features of LR.