The client should download all new blocks from the proxy machine.
The client does not download new blocks. Instead it logs in it's own debug log:
Ignoring getheaders from peer=0 because node is in initial block download
proxy node is running for hours without problems, downloading new blocks as they come.
2017-08-03 07:57:57 Bitcoin version v0.14.6.0-ga46e63c
2017-08-03 07:57:57 InitParameterInteraction: parameter interaction: -connect set -> setting -dnsseed=0
2017-08-03 07:57:57 InitParameterInteraction: parameter interaction: -listen=0 -> setting -upnp=0
2017-08-03 07:57:57 InitParameterInteraction: parameter interaction: -listen=0 -> setting -discover=0
2017-08-03 07:57:57 InitParameterInteraction: parameter interaction: -listen=0 -> setting -listenonion=0
2017-08-03 07:57:57 InitParameterInteraction: parameter interaction: -whitelistforcerelay=1 -> setting -whitelistrelay=1
2017-08-03 07:57:57 Assuming ancestors of block 000000000000000000ff3a41f208c932d5f91fe8d0739fca36152f6073b2ef5e have valid signatures.
2017-08-03 07:57:57 Default data directory /home/bitcoin/.bitcoin
2017-08-03 07:57:57 Using data directory /home/bitcoin/.bitcoin
2017-08-03 07:57:57 Using config file /home/bitcoin/.bitcoin/bitcoin.conf
2017-08-03 07:57:57 Using at most 125 automatic connections (1024 file descriptors available)
2017-08-03 07:57:57 Using 32 MiB out of 32 requested for signature cache, able to store 1048576 elements
2017-08-03 07:57:57 Using 0 threads for script verification
2017-08-03 07:57:57 scheduler thread start
2017-08-03 07:57:57 Allowing HTTP connections from: 127.0.0.0/8 ::1/128 x.x.x.x/32
2017-08-03 07:57:57 Binding RPC on address :: port 8332
2017-08-03 07:57:57 Binding RPC on address 0.0.0.0 port 8332
2017-08-03 07:57:57 Binding RPC on address 0.0.0.0 port 8332 failed.
2017-08-03 07:57:57 Initialized HTTP server
2017-08-03 07:57:57 HTTP: creating work queue of depth 16
2017-08-03 07:57:57 Starting RPC
2017-08-03 07:57:57 Starting HTTP RPC server
2017-08-03 07:57:57 Config options rpcuser and rpcpassword will soon be deprecated. Locally-run instances may remove rpcuser to use cookie-based auth, or may be replaced with rpcauth. Please see share/rpcuser for rpcauth auth generation.
2017-08-03 07:57:57 Registering HTTP handler for / (exactmatch 1)
2017-08-03 07:57:57 Starting HTTP server
2017-08-03 07:57:57 HTTP: starting 4 worker threads
2017-08-03 07:57:57 Using BerkeleyDB version Berkeley DB 5.3.28: (September 9, 2013)
2017-08-03 07:57:57 Using wallet wallet.dat
2017-08-03 07:57:57 init message: Verifying wallet...
2017-08-03 07:57:57 CDBEnv::Open: LogDir=/home/bitcoin/.bitcoin/database ErrorFile=/home/bitcoin/.bitcoin/db.log
2017-08-03 07:57:57 Entering http event loop
2017-08-03 07:57:57 Cache configuration:
2017-08-03 07:57:57 * Using 2.0MiB for block index database
2017-08-03 07:57:57 * Using 8.0MiB for chain state database
2017-08-03 07:57:57 * Using 440.0MiB for in-memory UTXO set (plus up to 286.1MiB of unused mempool space)
2017-08-03 07:57:57 init message: Loading block index...
2017-08-03 07:57:57 Opening LevelDB in /home/bitcoin/.bitcoin/blocks/index
2017-08-03 07:57:57 Opened LevelDB successfully
2017-08-03 07:57:57 Using obfuscation key for /home/bitcoin/.bitcoin/blocks/index: 0000000000000000
2017-08-03 07:57:57 Opening LevelDB in /home/bitcoin/.bitcoin/chainstate
2017-08-03 07:57:58 Opened LevelDB successfully
2017-08-03 07:57:58 Using obfuscation key for /home/bitcoin/.bitcoin/chainstate: 406d4b99b2383ee0
2017-08-03 07:58:02 LoadBlockIndexDB: last block file = 953
2017-08-03 07:58:02 LoadBlockIndexDB: last block file info: CBlockFileInfo(blocks=62, size=44456164, heights=478509...478570, time=2017-08-01...2017-08-02)
2017-08-03 07:58:02 Checking all blk files are present...
2017-08-03 07:58:02 LoadBlockIndexDB: transaction index disabled
2017-08-03 07:58:02 LoadBlockIndexDB: hashBestChain=000000000000000000e29f8c626dd806633e7fe23004126ab4ec157ad720660b height=478570 date=2017-08-02 03:15:01 progress=0.998642
2017-08-03 07:58:02 init message: Rewinding blocks...
2017-08-03 07:58:03 Committing 0 changed transactions (out of 0) to coin database...
2017-08-03 07:58:03 init message: Verifying blocks...
2017-08-03 07:58:03 Verifying last 6 blocks at level 3
2017-08-03 07:58:03 [0%]...[16%]...[33%]...[50%]...[66%]...[83%]...[99%]...[DONE].
2017-08-03 07:58:03 No coin database inconsistencies in last 7 blocks (2936 transactions)
2017-08-03 07:58:03 block index 5761ms
2017-08-03 07:58:03 Reading estimates: 98 buckets counting confirms up to 25 blocks
2017-08-03 07:58:03 init message: Loading wallet...
2017-08-03 07:58:03 nFileVersion = 140600
2017-08-03 07:58:03 Keys: 322 plaintext, 0 encrypted, 322 w/ metadata, 322 total
2017-08-03 07:58:03 Performing wallet upgrade to 60000
2017-08-03 07:58:03 wallet 7ms
2017-08-03 07:58:03 setKeyPool.size() = 300
2017-08-03 07:58:03 mapWallet.size() = 9
2017-08-03 07:58:03 mapAddressBook.size() = 19
2017-08-03 07:58:03 mapBlockIndex.size() = 478631
2017-08-03 07:58:03 nBestHeight = 478570
2017-08-03 07:58:03 init message: Loading addresses...
2017-08-03 07:58:03 ERROR: Read: Failed to open file /home/bitcoin/.bitcoin/peers.dat
2017-08-03 07:58:03 Invalid or missing peers.dat; recreating
2017-08-03 07:58:03 Flushed 0 addresses to peers.dat 1ms
2017-08-03 07:58:03 init message: Loading banlist...
2017-08-03 07:58:03 ERROR: Read: Failed to open file /home/bitcoin/.bitcoin/banlist.dat
2017-08-03 07:58:03 Invalid or missing banlist.dat; recreating
2017-08-03 07:58:03 Flushed 0 banned node ips/subnets to banlist.dat 1ms
2017-08-03 07:58:03 init message: Starting network threads...
2017-08-03 07:58:03 DNS seeding disabled
2017-08-03 07:58:03 init message: Done loading
2017-08-03 07:58:03 msghand thread start
2017-08-03 07:58:03 opencon thread start
2017-08-03 07:58:03 trying connection <IP OF PROXY>:8333 lastseen=0.0hrs
2017-08-03 07:58:03 addcon thread start
2017-08-03 07:58:03 net thread start
2017-08-03 07:58:03 Added connection to <IP OF PROXY>:8333 peer=0
2017-08-03 07:58:03 AddToWallet ....
2017-08-03 07:58:03 AddToWallet ....
2017-08-03 07:58:03 sending version (113 bytes) peer=0
2017-08-03 07:58:03 send version message: version 70015, blocks=478570, us=[::]:0, them=[::]:0, peer=0
2017-08-03 07:58:03 received: version (113 bytes) peer=0
2017-08-03 07:58:03 sending verack (0 bytes) peer=0
2017-08-03 07:58:03 sending getaddr (0 bytes) peer=0
2017-08-03 07:58:03 receive version message: /Bitcoin ABC:0.14.6(EB8.0)/: version 70015, blocks=478583, us=[::]:0, peer=0, peeraddr=<IP OF PROXY>:8333
2017-08-03 07:58:03 added time data, samples 2, offset +0 (+0 minutes)
2017-08-03 07:58:03 received: verack (0 bytes) peer=0
2017-08-03 07:58:03 sending sendheaders (0 bytes) peer=0
2017-08-03 07:58:03 sending sendcmpct (9 bytes) peer=0
2017-08-03 07:58:03 sending ping (8 bytes) peer=0
2017-08-03 07:58:03 sending feefilter (8 bytes) peer=0
2017-08-03 07:58:03 received: sendheaders (0 bytes) peer=0
2017-08-03 07:58:03 received: sendcmpct (9 bytes) peer=0
2017-08-03 07:58:03 received: ping (8 bytes) peer=0
2017-08-03 07:58:03 sending pong (8 bytes) peer=0
2017-08-03 07:58:03 received: getheaders (997 bytes) peer=0
2017-08-03 07:58:03 Ignoring getheaders from peer=0 because node is in initial block download
2017-08-03 07:58:03 received: pong (8 bytes) peer=0
2017-08-03 07:58:04 received: addr (30003 bytes) peer=0
2017-08-03 07:58:04 Added 1000 addresses from <IP OF PROXY>: 0 tried, 874 new
2017-08-03 07:58:05 received: inv (37 bytes) peer=0
[..]