I know before I say this that it will be very unpopular, but the available rooms for upgrade are identified by the property, not by the inventory one can see online. This means that the property (staff) decide what is or isn't available for complimentary upgrade, and not just in the general sense of always excluding certain suite types, but on-the-fly as well.

The inventory you see online is never the full story of what's going on with real time, actual inventory - thanks in no small part to hotel overselling being the industry standard.

​​​​​​When Elites are denied upgrades, even if the rooms appear available online, there are dozens of reasons why it could be happening, and waving the app around at a front desk agent rarely helps.

I'm sure most here don't need this explained, but your post did mention suites appearing available in the app, and this should never be any indication as to entitlement to a room upgrade.