When an image file (JPG, PNG, TIF, and so forth) is uploaded from a local machine and saved to 'My Content' within ArcGIS Online, the image is not given a hard-coded URL. Instead, the image is placed onto Amazon cloud servers where it continuously changes URLs. There are no URLs assigned to files uploaded to ArcGIS Online. Instead, the URLs are dynamic and designed for storage or sharing rather than hosting. The image's URL changes after a few minutes, which causes the image to disappear when hosted on a web map.
ArcGIS Online does allow users to publish data with hard-coded URLs, such as hosted feature services and tile services. To prevent an image file from disappearing, the image must be published online. Once an image file is added to ArcGIS Online and shared publicly, the details page displays the URL of the image. Use this URL to reference the image in web apps, web map pop-up windows, and so on.
If the image is to be used in an ArcGIS Online pop-up, configure the pop-up by entering a URL to an image stored on an external website with static URLs such as Dropbox or Photobucket. However, when an item is added from an external site, ArcGIS Online references the REST endpoint (URL) and does not store the item in ArcGIS Online itself.