Thank you very much for the reply Michael, I did try that to no avail.
However, I noticed from previous threads I reviewed to look at the spatial index. In my situation this time, the 'Rebuild Index' option from the item's description was not available and although it would let me access the button, it would not allow me to rebuild the index.
This then led me to try another method from AGO where I create a new layer and import the data and/or schema from the layer that is currently not cooperating. I had not previously attempted to create a layer from AGO and was surprised at the level of abilities there was available to do this.
I created a new layer from AGO and based the schema from the exiting data at creation and then imported the data into the resultant data shell. This process so far has worked very well for me in my current situation and I am now able to add the 1033 lines contained from within the created in AGO data layer, to the map and have it displayed correctly, without the dreaded orange triangle-"the layer did not draw completely".