Refreshing datasets from dataflows across other tenants

I have a setup that looks like this:

Tenant A

Dataset 1

Dataset 2

Dataset 3

Dataflow 1

Tenant B

Dataflow 2

Tenant C

Dataflow 3

Dataset 1 is fed from Dataflow 1 as both are on Tenant A. Up until yesterday, I had Dataset 2 refreshing from Dataflow 2 on Tenant B. Then, I added Dataset 3 which refreshes from Dataflow 3 on Tenant C.

Here's where things start to get funny:

1. If I log in on the scheduled refresh screen to Tenant B, then Dataset 2 refreshes from Dataflow 2 without a problem. 
2. If I log in to Tenant C, then Dataset 3 refreshes from Dataflow 3 without a problem, but Dataset 2's link to Dataflow 2 (on Tenant B) breaks. The error message is always the same: "The key didn't match any rows in the table. Table: XXXXX"
3. If I go back to Dataset 2 and into Tenant B, then Dataset 2 works again, but Dataset 3 which refreshes off Dataflow 3 on Tenant C breaks, yielding the same error message.

It would appear that where my datasets are pulling from different dataflows across different tenants, that I can only be logged into one of them at any given time. Has anyone else encountered this problem?