Filtering the log:
$ egrep -i "<4>|<8>|<16>|<32>|error|status|critical|fatal|sever|fail|cannot|unable" 061615_00001.log | grep -iv "status 0"
13:32:21.656 [1712.2216] <4> create_tpreq_file: {7,0,0,0}
13:33:57.640 [1192.744] <4> db_getSTUNIT: emmserver_name = epany-archive
13:33:57.640 [1192.744] <4> db_getSTUNIT: emmserver_port = 1556
13:35:02.859 [2652.2688] <2> db_error_add_to_file: dberrorq.c:midnite = 1434409200
13:35:02.859 [2652.2688] <4> read_backup: begin reading backup id epany-archive_1434382187 (duplicate), copy 1, fragment 1 from media id A001L2 on drive index 1
13:36:00.187 [1192.744] <2> db_error_add_to_file: dberrorq.c:midnite = 1434409200
13:36:00.187 [1192.744] <8> io_position_for_write: cannot locate on drive index 2, No more data is on the tape.
13:36:24.015 [1192.744] <2> io_read_block: read error on media id A00010, drive index 2 reading header block, len = 0; No more data is on the tape. (1104)
13:36:24.203 [1192.744] <2> io_read_block: read error on media id A00010, drive index 2 reading header block, len = 0; No more data is on the tape. (1104)
13:36:24.406 [1192.744] <2> io_read_block: read error on media id A00010, drive index 2 reading header block, len = 0; No more data is on the tape. (1104)
13:36:24.609 [1192.744] <2> io_read_block: read error on media id A00010, drive index 2 reading header block, len = 0; No more data is on the tape. (1104)
13:36:24.828 [1192.744] <2> io_read_block: read error on media id A00010, drive index 2 reading header block, len = 0; No more data is on the tape. (1104)
13:36:25.062 [1192.744] <2> io_read_block: read error on media id A00010, drive index 2 reading header block, len = 0; No more data is on the tape. (1104)
13:36:25.062 [1192.744] <2> db_error_add_to_file: dberrorq.c:midnite = 1434409200
13:36:25.062 [1192.744] <16> io_position_for_write: cannot position media id A00010 for write
13:36:25.062 [1192.744] <2> send_MDS_msg: DEVICE_STATUS 1 113 epany-archive A00010 4000020 HP.ULTRIUM6-SCSI.000 2000006 POSITION_ERROR 0 0
13:36:25.062 [1192.744] <2> log_media_error: successfully wrote to error file - 06/16/15 13:36:25 A00010 2 POSITION_ERROR HP.ULTRIUM6-SCSI.000
13:36:25.062 [1192.744] <2> check_error_history: just tpunmount: called from bptm line 20233, EXIT_Status = 86
13:36:25.062 [1192.744] <2> bptm: EXITING with status 86 <----------
13:36:25.062 [2652.2688] <2> read_data: received exit status 86 from write side of duplicate
13:36:25.093 [2652.2688] <2> check_error_history: just tpunmount: called from bptm line 12149, EXIT_Status = 86
13:36:27.750 [2944.492] <4> create_tpreq_file: {7,0,0,0}
13:39:27.875 [1904.1964] <4> create_tpreq_file: {6,0,0,0}
.
It's definitely failing to write to media A00010.
.
Perhaps try a backup to it?
Can you expire what is already on A00010, then bpexpdate -deassignempty, and then create a temporary pool, and then assign this media to that pool, and then create a dummy backup job to write to that pool, so that it selects A00010, and try a big backup perhaps. Or try two small backups of the same job/policy, one after another, and see if the second backup job also fails to append to the same media?