Micro SDHC Card Reader

Some time ago, I tried to read a Memory Stick Pro Duo card (via Memory Stick adapter) on an old card reader that is compatible with Memory Stick only. The result was obvious: the card reader wouldn't read the MS-D card. I ended up finding an MSD-compliant card reader to have the task done.
I think similar things happen here. IMO The step-up adapter is just a medium (I could be wrong though, so go double-check); the most crucial part is to have a truly SDHC-compatible card reader (or device) handy.
I suggest you get a card reader that is SDHC compatible. Plug your micro-SDHC card directly to the card reader to see if it is recognisable. Then, put the card into the step-up adapter, then have the same card reader read the "SD" card. If the card fails to be read, then perhaps there is a problem with your step-up adapter.