Probably time to configure your test client to really used ftpes

... in FileZilla, create a new host entry, and select Encryption: Require explicit FTP over TLS...
Client:
FileZilla Client
----------------
Version: 3.4.0
Build information:
Compiled for: i586-pc-mingw32msvc
Compiled on: x86_64-unknown-linux-gnu
Build date: 2011-03-27
Compiled with: i586-mingw32msvc-gcc (GCC) 4.2.1-sjlj (mingw32-2)
Compiler flags: -g -O2 -Wall -g -fexceptions
Linked against:
wxWidgets: 2.8.12
GnuTLS: 2.10.4
Operating system:
Name: Windows Server 2003 (build 3790, Service Pack 2)
Version: 5.2
Platform: 32 bit system
Server: QNAP TS-509 Pro Version 3.4.2 build 0331T
Case 1 - normal:
Closed session and FIleZille, login, then get file:
Status: Resolving address of ts-509pro
Status: Connecting to 10.10.1.109:21...
Status: Connection established, waiting for welcome message...
Response: 220 NASFTPD Turbo station 2.x 1.3.2e Server (ProFTPD) [::ffff:10.10.1.109]
Command: AUTH TLS
Response: 234 AUTH TLS successful
Status: Initializing TLS...
Status: Verifying certificate...
Command: USER user
Status: TLS/SSL connection established.
Response: 331 Password required for user
Command: PASS ********
Response: 230 User user logged in
Command: OPTS UTF8 ON
Response: 200 UTF8 set to on
Command: PBSZ 0
Response: 200 PBSZ 0 successful
Command: PROT P
Response: 200 Protection set to Private
Status: Connected
Status: Starting download of /Public/4gb
Command: CWD /Public
Response: 250 CWD command successful
Command: PWD
Response: 257 "/Public" is the current directory
Command: TYPE A
Response: 200 Type set to A
Command: PASV
Response: 227 Entering Passive Mode (10,10,1,109,217,66).
Command: RETR 4gb
Response: 150 Opening ASCII mode data connection for 4gb (4294967296 bytes)
Error: GnuTLS error -37: Rehandshake was requested by the peer.
Error: Could not read from transfer socket: ECONNABORTED - Connection aborted
Response: 450 Transfer aborted. Link to file server lost
Error: File transfer failed after transferring 1'073'741'824 bytes in 72 seconds
...
Case 2 - Rehandshake requested every single GB tranfered - why ever, FileZilla is (under some conditions) able to continue retrieving the file using the continuation capabilities. However, QNAP can't build in this likely specific FileZilla case:
Status: Resolving address of ts-509pro
Status: Connecting to 10.10.1.109:21...
Status: Connection established, waiting for welcome message...
Response: 220 NASFTPD Turbo station 2.x 1.3.2e Server (ProFTPD) [::ffff:10.10.1.109]
Command: AUTH TLS
Response: 234 AUTH TLS successful
Status: Initializing TLS...
Status: Verifying certificate...
Command: USER user
Status: TLS/SSL connection established.
Response: 331 Password required for user
Command: PASS ********
Response: 230 User user logged in
Command: SYST
Response: 215 UNIX Type: L8
Command: FEAT
Response: 211-Features:
Response: MDTM
Response: MFMT
Response: UTF8
Response: AUTH TLS
Response: MFF modify;UNIX.group;UNIX.mode;
Response: MLST modify*;perm*;size*;type*;unique*;UNIX.group*;UNIX.mode*;UNIX.owner*;
Response: LANG en-US*
Response: PBSZ
Response: PROT
Response: REST STREAM
Response: SIZE
Response: 211 End
Command: OPTS UTF8 ON
Response: 200 UTF8 set to on
Command: PBSZ 0
Response: 200 PBSZ 0 successful
Command: PROT P
Response: 200 Protection set to Private
Status: Connected
Status: Retrieving directory listing...
Command: PWD
Response: 257 "/" is the current directory
Command: TYPE I
Response: 200 Type set to I
Command: PASV
Response: 227 Entering Passive Mode (10,10,1,109,220,125).
Command: MLSD
Response: 150 Opening ASCII mode data connection for MLSD
Response: 226 Transfer complete
Status: Directory listing successful
Status: Retrieving directory listing...
Command: CWD Public
Response: 250 CWD command successful
Command: PWD
Response: 257 "/Public" is the current directory
Command: PASV
Response: 227 Entering Passive Mode (10,10,1,109,218,144).
Command: MLSD
Response: 150 Opening ASCII mode data connection for MLSD
Response: 226 Transfer complete
Status: Directory listing successful
Status: Resolving address of ts-509pro
Status: Connecting to 10.10.1.109:21...
Status: Connection established, waiting for welcome message...
Response: 220 NASFTPD Turbo station 2.x 1.3.2e Server (ProFTPD) [::ffff:10.10.1.109]
Command: AUTH TLS
Response: 234 AUTH TLS successful
Status: Initializing TLS...
Status: Verifying certificate...
Command: USER user
Status: TLS/SSL connection established.
Response: 331 Password required for user
Command: PASS ********
Response: 230 User user logged in
Command: OPTS UTF8 ON
Response: 200 UTF8 set to on
Command: PBSZ 0
Response: 200 PBSZ 0 successful
Command: PROT P
Response: 200 Protection set to Private
Status: Connected
Status: Starting download of /Public/soundeffects.rar
Command: CWD /Public
Response: 250 CWD command successful
Command: PWD
Response: 257 "/Public" is the current directory
Command: TYPE I
Response: 200 Type set to I
Command: PASV
Response: 227 Entering Passive Mode (10,10,1,109,219,93).
Command: RETR soundeffects.rar
Response: 150 Opening BINARY mode data connection for soundeffects.rar (2565961553 bytes)
Error: GnuTLS error -37: Rehandshake was requested by the peer.
Error: Could not read from transfer socket: ECONNABORTED - Connection aborted
Response: 450 Transfer aborted. Link to file server lost
Error: File transfer failed after transferring 1'073'741'824 bytes in 73 seconds
Status: Starting download of /Public/soundeffects.rar
Command: PASV
Response: 227 Entering Passive Mode (10,10,1,109,220,115).
Command: REST 1073741824
Response: 350 Restarting at 1073741824. Send STORE or RETRIEVE to initiate transfer
Command: RETR soundeffects.rar
Response: 150 Opening BINARY mode data connection for soundeffects.rar (1492219729 bytes)
Error: GnuTLS error -37: Rehandshake was requested by the peer.
Error: Could not read from transfer socket: ECONNABORTED - Connection aborted
Response: 450 Transfer aborted. Link to file server lost
Error: File transfer failed after transferring 1'073'741'824 bytes in 75 seconds
Status: Starting download of /Public/soundeffects.rar
Status: Testing resume capabilities of server
Command: PASV
Response: 227 Entering Passive Mode (10,10,1,109,220,88).
Command: REST 2565961552
Response: 350 Restarting at 2565961552. Send STORE or RETRIEVE to initiate transfer
Command: RETR soundeffects.rar
Response: 150 Opening BINARY mode data connection for soundeffects.rar (1 bytes)
Response: 226 Transfer complete
Command: PASV
Response: 227 Entering Passive Mode (10,10,1,109,220,68).
Command: REST 2147483648
Response: 350 Restarting at 2147483648. Send STORE or RETRIEVE to initiate transfer
Command: RETR soundeffects.rar
Response: 150 Opening BINARY mode data connection for soundeffects.rar (418477905 bytes)
Response: 226 Transfer complete
Status: File transfer successful, transferred 418'477'905 bytes in 29 seconds
Case 3:
On the control session disconnection, the TLS session is STILL not correctly shutdown - just let the (ftpes) connection idle for ten minutes and you will see this:
...
Response: 421 Idle timeout (600 seconds): closing control connection
Error: GnuTLS error -9: A TLS packet with unexpected length was received.
Status: Server did not properly shut down TLS connection
Error: Could not read from socket: ECONNABORTED - Connection aborted
Error: Disconnected from server