This is a well-known problem with the Moto G (we're talking about the 4G LTE version here, since the original G doesn't have a Micro SD slot). There are numerous threads related to this issue on other Android sites as well as on Motorola's site.
Supposedly Motorola is exploring a software patch to address it... but I'm not sure it is addressable. In my personal opinion it is a hardware flaw - some phones may have faulty micro SD readers. Why do I think this? I own 3 Moto 4G LTE handsets and 4 class 10 32 GB micro SD cards. Any of the micro SD cards will work in 2 of the 3 handsets. In the 3rd handset, I cannot get ANY of the 32 GB MicroSD to work. I will get error messages "MicroSD has been removed, please replace" or other messages (including the "card needs to be formatted / checking card" loop). You name it I have tried it, including reformatting on my PC, etc. I can take a 32 GB MicroSD from the phone where it won't work, and move it directly to one of the other phones, and it works fine. Move it back to the first phone and it will not work.
Note that in the non-working phone, I CAN mount a lower level MicroSD. I currently have a sad little 2GB card in there that works fine. But it is strange to see two phones with 32GB cards, and one that won't work with the exact same cards. I am on my way to the store to pick up a 16GB card to see if that will work...