Joanne, I found some of your profiles on Wikitree and did a search on Issom Robertson, (another son of Robert) since he has such an unusual name that I had some hope of locating him. On the 1900 US census for Knox County, Illinois, he states that he was born in Kentucky, but his mother and father were born in South Carolina. His birthday is listed as November of 1825, (You have August 29, so that's a discrepancy) and he's working on his second marriage. I imagine this could be someone other than the son of Robert Robertson, but Isom (Issom) seems like such an unusual name I thought it was a pretty likely possibility.
Here's what the census says:
Isom Robertson Male age 75 Married White Head 2nd marriage, birth month & year Nov 1825, born in Kentucky, Father born in South Carolina; Mother born in South Carolina
"United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/3:1:S3HT-DCS7-2HY?cc=1325221&wc=9BQF-BZ7%3A1030552601%2C1031356301%2C1035750101 : 5 August 2014), Illinois > Knox > ED 39 Galesburg Township Galesburg city Ward 3 > image 15 of 32; citing NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, n.d.).
I know this doesn't answer the question about Robert, but it gives a starting point for a more focused search (South Carolina).
Hope this helps.