Possibly. My uncle cut his SIM card to nano size, too, and he's having all sorts of problems with it (messages and calls not going through, network dropping out, etc). He's been looking to replace his current SIM with an actual nano SIM, unfortunately, his carrier is all out of stock.I took the Straighttalk sim card out of my iPhone 4 and cut it down to a nano size. It was instantly recognized when I put it in the iPhone 5.
Is this a problem with my Sim card? The one I modified to reduce it to nano size.
Mind, some carriers do require a SIM card that has been provisioned for LTE. Maybe your SIM is not LTE compatible to begin with.