Likely, your map is too big for the web browser. Have you added more than one layer to your map? Even though you adhere to the 1000 feature limit, some web browsers can't handle drawing all of the features. From the symptoms you describe, I would guess that you are using Internet Explorer version 8 or earlier. But, all web browsers will start to get overwhelmed if you try to add lots of layers to them.
You can try using a different web browser, like chrome or firefox. If you're already doing that, you can try generalizing your features before you add them to a web map. Polygon and line data often have a lot of vertices, and these are all drawn by the web browser. Often, you can generalize the data without losing precision.
If you share your map with everyone then post a link to it, I can look at it.
Thanks,
Mike