I'm working with Tony on this project. We realized the table does show attachments are enabled and that's where the images are stored so disregard Tony's question. What we have discovered is that images are being saved but we are unable to view them in ArcGIS online. If we export the feature service to a FGDB we can view the images in ArcMap. However if we use the map that is created when we publish the form we have noticed that the related "repeat" table does not show in the details tab and we can not view photos. We also tried creating a new map and adding the feature service which does pull in the related table but again were unsuccessful at viewing images.
We used the sample form in the XML documentation in the Repeats section. This form gave us very similar behavior in that the default map created by publishing the form did not allow us to view images but when we added the feature service to a new map the related layer was also added and this time we were successful in viewing the images in AGO. The difference here is that the sample form used a geo location point and created the "repeat" table as a layer instead of a table.
This issue only exists when using the image type in the repeat function. We do not have any problems viewing photos in AGO when not using the repeat.