Car is losing coolant from the transaxle coolant hose?
You have a leak. You've identified where the leak is coming from. Now you're supposed to fix it.
The coolant reservoir recovery system doesn't work when you have a leak because the leak doesn't allow the system to build up pressure or vacuum to move the coolant from the reservoir to the radiator.
On last thing, when you say %26quot;On top of that my coolant reservoir remains full and seems to be leaking as well.%26quot;
It remains full but seems to be leaking sounds contradictory.