To reproduce:

Add a RadRichTextBox, type some text and a few new lines(by pressing Enter), enter some more text. Now export the document to a string using TxtFormatProvider then Import it. You will notice that the new lines are missing.

Workaround:
Use the following Import method:

public RadDocument Import(string input)
{
    RadDocument document = new RadDocument();

    Section section = new Section();
    document.Sections.Add(section);

    string[] paragraphs = GetParagraphsFromText(input);
    for (int i = 0; i < paragraphs.Length; i++)
    {
        if (string.IsNullOrEmpty(paragraphs[i]))
        {
            paragraphs[i] = DocumentEnvironment.NewLine;
        }

        Paragraph paragraph = new Paragraph();
        section.Blocks.Add(paragraph);
        Span span = new Span(paragraphs[i]);
        paragraph.Inlines.Add(span);
    }

    return document;
}

private string[] GetParagraphsFromText(string input)
{
    return this.CleanUpNewLines(input).Split(new string[] { Environment.NewLine }, StringSplitOptions.None);
}

private string CleanUpNewLines(string str)
{
    StringBuilder result = new StringBuilder(str.Length);
    bool hasSeenCr = false;

    for (int i = 0, l = str.Length; i < l; ++i)
    {
        if (str[i] == '\r')
        {
            if (hasSeenCr)
            {
                result.Append(DocumentEnvironment.NewLine);
            }

            hasSeenCr = true;
        }
        else if (str[i] == '\n')
        {
            result.Append(DocumentEnvironment.NewLine);
            hasSeenCr = false;
        }
        else
        {
            if (hasSeenCr)
            {
                result.Append(DocumentEnvironment.NewLine);
                hasSeenCr = false;
            }

            result.Append(str[i]);
        }
    }

    if (hasSeenCr)
    {
        result.Append(DocumentEnvironment.NewLine);
    }

    return result.ToString();
}


Resolution: 
This issue is addressed in the new version of the control - RadRichTextEditor. Please use the new control instead the RadRichTextBox.