There are three separate systems involved, and almost every bug in this stack comes from an assumption that two of them agree on a piece of data when they actually don't:

• Your extension's package manifest — the XML file Joomla reads on install, and the one it copies into administrator/manifests/packages/ for later reference.
• Akeeba Release System (ARS) — hosts your release files and generates the update-stream XML feed that Joomla's Extensions: Update page polls. ARS is also the gatekeeper: it decides, per download request, whether the requester is allowed to have the file.
• Your storefront (J2Commerce, or whatever you use) — issues the actual Download ID / license key to a paying customer, and needs some way to tell ARS "this specific customer's key should be allowed to access this specific product's protected releases."

Customer's Joomla site
  │
  │ 1. "Check for Updates"  (Joomla's Updater service)
  ▼
Your update stream URL  (hosted by ARS, e.g. https://yoursite.com/updates/yourpkg.xml)
  │
  │ 2. Feed lists latest version + download URL + <element>
  ▼
Joomla matches <element> against the installed extension's real element
  │
  │ 3. If matched: appends the customer's Download ID (extra_query) and downloads
  ▼
ARS checks the download request against the Item's Access Level
  │
  │ 4. Valid key + sufficient access → 200 + file.  Otherwise → 403.
  ▼
Joomla installs the package

Every step above is a place we found a real, silent failure. We'll go through them in the order you're most likely to hit them.