Although the card works across dimensions (including custom dimensions) it doesn't inside a compact machine.

Is the network loaded?
there shouldn't be anything special about the compact machines dimension

Chunk? yes.....
The inventory shows briefly then disappears

I have seen this issue before, but I don't quite know what causes it.

there are two options I can think of:

1. Your network doesn't have enough power / it uses more power in a tick than it can store (one dense cell would be enough)
2. the chunk loading doesn't work correctly and it unloads at least some parts of the network

Spot on, one dense cell and issue resolved, thanks.

(Weird that it's ok in other dimensions though /shrug)