I have not worked on the 7 plus yet but have had this issue with several of the 6 plus iphones...both of which require board level repair. 1st repair is to replace the Tristar (U2) charging IC Chip and 2nd is to verify proper voltage on NAND (Hard Drive) (Reball has helped).
It could be a software issue as well I imagine but if you are not able to restore, have restored with same issue, or get an error message on Itunes, I think your best bet is to take it to a good repair shop or to Apple if under warranty.