Getting to the previous paragraph

I would go a different way:

Remember: there can be more than one graphic in an frame.

That can be the reason, why your second loop doesn't work, because when you delete a frame with multiple graphics in it then NextGraphicInDoc won't work.

My way would be: gather all Frames with Insets in an array. Then delete these frames.

If one Frame contains multiple graphics I would gather their names in a string.

    var oDoc, oGraphic,  gaFrames=[];  
    var oGraphicObject;
    
    oDoc = app.ActiveDoc;  
    
    if (oDoc.ObjectValid())
        {
        GatherGraphics(oDoc);
        
        DeleteGraphics(oDoc);
        }
    else 
        {
        alert("No active Document");    
        }

function GatherGraphics(doc)
{ 
     var graphic = doc.FirstGraphicInDoc;
     
     while (graphic) 
        {
         if (graphic.type == Constants.FO_Inset)
            {
             gaFrames.push(graphic.FrameParent);
             }
         graphic = graphic.NextGraphicInDoc;
      }
 }

function DeleteGraphics(doc)
{
    var pgf, sText="";
    
    for(i = 0; i < gaFrames.length; i++)
        {
        sText = CreateText(gaFrames[i]);
        
        pgf = gaFrames[i].TextLoc.obj.PrevPgfInFlow;
        tl = new TextLoc(pgf, Constants.FV_OBJ_END_OFFSET-1);

        doc.AddText(tl, "[GRAPHIC]: " + sText);
        
        gaFrames[i].Delete();
        }
}

function CreateText(fFrame)
{
    var graphic = fFrame.FirstGraphicInFrame;
    var sText = "";
    var aText = [];
    
    // if more than 1 Inset in 1 Frame
    while (graphic.ObjectValid()) 
        {
         aText.push(graphic.InsetFile);
         graphic = graphic.NextGraphicInFrame;
        }
    
    return sText = aText.join("--");    
}

By the way, great job in separating your tasks into functions.

I am pressed for time but I will give you this:

// Store the anchored frame's paragraph object.

pgf = frame.TextLoc.obj;

// Get the previous paragraph in the flow.

pgf = pgf.PrevPgfInFlow;