This sounds familiar to something we had been dealing with also, although not exactly, but you are on the right track with the HTTP vs HTTPS issues. This was what we had to change in order to get everything working together nicely. What we learned was that our AGOL account or portal is setup in HTTPS. So in order for any of our published mapservices or feature services to work in AGOL; we had to migrate our server side to HTTPS as well. We initiated our ArcServer with just HTTP, as we thought we were secure enough behind the corporate firewall. AGOL and your Server both need to be the same to work together. We ended up creating a Local CA certificate rather than buying one from VeriSign. All of our services are behind our corporate firewall which is "secure" but we still needed to migrate all of our mapservices to HTTPS to get anything working in AGOL and the AppBuilder. We were finally able to make and release App's after that migration. We are using the ArcGIS Viewer for Silverlight - Application Builder. Try different browsers as well. We noticed more issues with chrome, so we have been testing in FireFox. What version of ArcServer you are running? Hope this helps.
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