As suggested by Martin Choma, I've added debug logging using "-Djavax.net.debug=ssl,handshake". Now, I get a whole bunch of logging that I don't really understand. Here is what I think is the relevant logging just prior to the error happening:
2017-03-21 09:45:54,957 INFO [stdout] (Thread-99) ***
2017-03-21 09:45:54,968 INFO [stdout] (Thread-99) Found trusted certificate:
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) [
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) [
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) Version: V3
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) Subject: CN=zzzzzzzzz, O=yyyyyyyy, C=US
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) Signature Algorithm: MD5withRSA, OID = 1.2.840.113549.1.1.4
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99)
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) Key: Sun RSA public key, 1024 bits
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) modulus: 149768031229355317819669627003541010970188409896072123942659823055749257442913555306139263532680887521476069480498423244630043039059932665046536606777806669151992913044418121042873068648955756669726859500240051803178353300912112534643112797025626661774438729388377935143233681906223561041770767373053814591257
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) public exponent: 65537
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) Validity: [From: Wed Jun 07 15:39:09 MST 2006,
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) To: Tue Apr 14 15:39:09 MST 2026]
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) Issuer: CN=zzzzzzzzzz, O=yyyyyyyyy, C=US
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) SerialNumber: [ 4488a70d]
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99)
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) ]
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) Algorithm: [MD5withRSA]
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) Signature:
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) 0000: 7E FD B5 99 18 7C 58 B6 19 63 80 EA 16 8B 1F BD ......X..c......
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) 0010: 2F 23 B9 ED 91 53 B4 11 6F 35 B4 02 F5 24 D6 EE /#...S..o5...$..
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) 0020: BA 3E 5B FA BC 0D 74 9E 43 02 BE A9 D7 5B B6 71 .>[...t.C....[.q
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) 0030: 99 C8 F9 40 B6 C1 04 E8 35 AA 3E 40 30 66 65 FC ...@....5.>@0fe.
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) 0040: 4A 4B 8A 9B B7 C9 B7 93 F6 C5 57 03 DE 9C F4 7F JK........W.....
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) 0050: 91 92 1E 17 F4 1D 17 4A 80 11 61 85 B0 06 5D 8C .......J..a...].
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) 0060: 25 C0 56 E9 6F DB 80 35 94 0D BF 53 85 1E D5 15 %.V.o..5...S....
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) 0070: 61 9F BA B5 6F 1F 5E 00 E7 43 76 41 C1 01 E4 F1 a...o.^..CvA....
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99)
2017-03-21 09:45:54,969 INFO [stdout] (Thread-99) ]
2017-03-21 09:45:54,970 INFO [stdout] (Thread-99) *** ServerHelloDone
2017-03-21 09:45:54,973 INFO [stdout] (Thread-99) *** ClientKeyExchange, RSA PreMasterSecret, TLSv1.1
2017-03-21 09:45:54,973 INFO [stdout] (Thread-99) Thread-99, WRITE: TLSv1.1 Handshake, length = 134
2017-03-21 09:45:54,973 INFO [stdout] (Thread-99) SESSION KEYGEN:
2017-03-21 09:45:54,973 INFO [stdout] (Thread-99) PreMaster Secret:
2017-03-21 09:45:54,974 INFO [stdout] (Thread-99) 0000: 03 03 B0 FE B7 4F C0 4D 8F 0F C3 1C CF 5F A8 ED .....O.M....._..
2017-03-21 09:45:54,974 INFO [stdout] (Thread-99) 0010: 80 89 5B 6D 6F CD 6D 64 CC E1 48 7D 29 3A C0 86 ..[mo.md..H.):..
2017-03-21 09:45:54,975 INFO [stdout] (Thread-99) 0020: 9E 72 06 52 07 86 EA DC AC BB 39 55 D1 0E 69 79 .r.R......9U..iy
2017-03-21 09:45:54,980 INFO [stdout] (Thread-99) CONNECTION KEYGEN:
2017-03-21 09:45:54,980 INFO [stdout] (Thread-99) Client Nonce:
2017-03-21 09:45:54,980 INFO [stdout] (Thread-99) 0000: 58 D1 58 C2 5C 2A 29 17 C9 D6 D9 4A 08 21 DE 42 X.X.\*)....J.!.B
2017-03-21 09:45:54,980 INFO [stdout] (Thread-99) 0010: 5E 0D 7B 88 6D 4D 04 5E 49 6F 40 84 9B 1C AC E5 ^...mM.^Io@.....
2017-03-21 09:45:54,981 INFO [stdout] (Thread-99) Server Nonce:
2017-03-21 09:45:54,981 INFO [stdout] (Thread-99) 0000: 00 00 00 C2 8B A1 1C B7 A6 DC A0 10 D8 39 EE 21 .............9.!
2017-03-21 09:45:54,982 INFO [stdout] (Thread-99) 0010: 2F 7F FC 66 9B 1D B8 E1 A7 27 62 66 1E E3 36 D4 /..f.....'bf..6.
2017-03-21 09:45:54,982 INFO [stdout] (Thread-99) Master Secret:
2017-03-21 09:45:54,983 INFO [stdout] (Thread-99) 0000: 80 CF C9 67 A8 D5 26 36 25 87 B8 01 3E 4D 30 0B ...g..&6%...>M0.
2017-03-21 09:45:54,983 INFO [stdout] (Thread-99) 0010: 7C DB 55 3C FF 3E 6F 33 BA E3 1C 89 A1 41 8F 61 ..U<.>o3.....A.a
2017-03-21 09:45:54,984 INFO [stdout] (Thread-99) 0020: BA DB 3C B5 03 A4 6C 6B F0 EE 2A 3B 72 F6 79 0D ..<...lk..*;r.y.
2017-03-21 09:45:54,984 INFO [stdout] (Thread-99) Client MAC write Secret:
2017-03-21 09:45:54,985 INFO [stdout] (Thread-99) 0000: 42 82 CB C4 68 EE 6A 20 14 97 26 90 D8 B7 A5 28 B...h.j ..&....(
2017-03-21 09:45:54,985 INFO [stdout] (Thread-99) 0010: 2C 5C 58 C0 ,\X.
2017-03-21 09:45:54,985 INFO [stdout] (Thread-99) Server MAC write Secret:
2017-03-21 09:45:54,986 INFO [stdout] (Thread-99) 0000: CC F4 2C 49 F0 53 79 22 99 8E 09 0F E2 43 0A DD ..,I.Sy".....C..
2017-03-21 09:45:54,986 INFO [stdout] (Thread-99) 0010: A2 A5 F1 F4 ....
2017-03-21 09:45:54,986 INFO [stdout] (Thread-99) Client write key:
2017-03-21 09:45:54,987 INFO [stdout] (Thread-99) 0000: D0 48 B8 BA 89 C6 72 C4 92 BB 3B D8 7D 1B 00 BF .H....r...;.....
2017-03-21 09:45:54,987 INFO [stdout] (Thread-99) Server write key:
2017-03-21 09:45:54,988 INFO [stdout] (Thread-99) 0000: 8A B9 E0 2C DD B9 DA 97 02 02 C0 63 9D 7A 2F A5 ...,.......c.z/.
2017-03-21 09:45:54,988 INFO [stdout] (Thread-99) ... no IV derived for this protocol
2017-03-21 09:45:54,989 INFO [stdout] (Thread-99) Thread-99, WRITE: TLSv1.1 Change Cipher Spec, length = 1
2017-03-21 09:45:54,991 INFO [stdout] (Thread-99) *** Finished
2017-03-21 09:45:54,991 INFO [stdout] (Thread-99) verify_data: { 72, 68, 241, 201, 139, 148, 155, 212, 114, 170, 87, 236 }
2017-03-21 09:45:54,991 INFO [stdout] (Thread-99) ***
2017-03-21 09:45:54,991 INFO [stdout] (Thread-99) Thread-99, WRITE: TLSv1.1 Handshake, length = 64
2017-03-21 09:45:54,992 INFO [stdout] (Thread-99) Thread-99, READ: TLSv1.1 Change Cipher Spec, length = 1
2017-03-21 09:45:54,993 INFO [stdout] (Thread-99) Thread-99, READ: TLSv1.1 Handshake, length = 64
2017-03-21 09:45:54,994 INFO [stdout] (Thread-99) *** Finished
2017-03-21 09:45:54,994 INFO [stdout] (Thread-99) verify_data: { 81, 220, 109, 100, 71, 72, 36, 254, 157, 248, 81, 248 }
2017-03-21 09:45:54,994 INFO [stdout] (Thread-99) ***
2017-03-21 09:45:54,995 INFO [stdout] (Thread-99) %% Cached client session: [Session-1, TLS_RSA_WITH_AES_128_CBC_SHA]
2017-03-21 09:45:54,995 INFO [stdout] (default task-54) default task-54, WRITE: TLSv1.1 Application Data, length = 192
2017-03-21 09:45:54,999 INFO [stdout] (Thread-99) Thread-99, received EOFException: ignored
2017-03-21 09:45:54,999 INFO [stdout] (Thread-99) Thread-99, called closeInternal(false)
2017-03-21 09:45:54,999 INFO [stdout] (Thread-99) Thread-99, SEND TLSv1.1 ALERT: warning, description = close_notify
2017-03-21 09:45:55,000 INFO [stdout] (Thread-99) Thread-99, WRITE: TLSv1.1 Alert, length = 48
2017-03-21 09:45:55,000 INFO [stdout] (Thread-99) Thread-99, called closeSocket(false)
2017-03-21 09:45:55,000 INFO [stdout] (Thread-99) Thread-99, called close()
2017-03-21 09:45:55,000 INFO [stdout] (Thread-99) Thread-99, called closeInternal(true)
2017-03-21 09:45:55,003 WARN [org.jboss.jca.core.connectionmanager.pool.strategy.OnePool] (default task-54) IJ000604: Throwable while attempting to get a new connection: null: javax.resource.ResourceException: zzzzzzzzzzzzzz:636; socket closed
Any clue what all this means?