The fact that no errors are reported does not mean that the records were deleted, but only that, in this case, no records matching the "Where" clause were found.
You don't need all that "Do While" loop to delete those records, the following line is sufficient (and necessary):
DB.ExecNonQuery2("Delete From LogRecord where LogDate = ?", Array As Object(RecordDated))
Check the number of records that meet that condition, before and after deletion:
Dim NumOfRecs As Int
NumOfRecs = DB.ExecQuerySingleResult2("SELECT COUNT(*) FROM LogRecord WHERE LogDate = ?", Array As Object(RecordDated))
Log(NumOfRecs)