いつもお世話になっております。

◆環境
Zabbix2.0.3、RHEL5.5、mysql5.0.77
server01：Zabbixサーバ
hogehoge01,02,03：監視対象サーバ

現在、上記環境でZabbixサーバを稼働させているのですが、
zabbix_server.logに下記ログが出力されております。
サーバは落ちておらず、監視アイテムの値も取得出来ております。
mysqld.logには何も出力されていませんでした。

------------------------------------------------------------------------------
29076:20130101:073051.549 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29080:20130101:104733.288 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge02' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29078:20130101:175852.413 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29076:20130101:200452.406 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29076:20130102:055652.944 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29084:20130102:102052.761 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29080:20130103:045653.411 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29078:20130103:135734.364 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge02' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29078:20130104:064654.242 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29082:20130104:162254.497 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29080:20130105:004654.354 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29076:20130106:014055.188 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29082:20130106:204856.520 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29078:20130107:013655.709 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29082:20130107:102142.007 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge02' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29076:20130107:120857.583 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29084:20130107:152617.195 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='server01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29076:20130107:220457.519 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29078:20130108:080458.410 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='hogehoge01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
29084:20130108:081618.345 [Z3005] query failed: [2006] MySQL server has gone away [select hostid,status from hosts where host='server01' and status in (0,1) and proxy_hostid is null and hostid between 0 and 99999999999999]
------------------------------------------------------------------------------

my.cnfの編集も行っております。
------
innodb_file_per_table
innodb_buffer_pool_size=512M
innodb_log_file_size=64M
default-character-set=utf8
------

wait_timeout値はデフォルトのままです。
# mysql -u root -e 'show variables like "wait_timeout"'
+---------------+-------+
| Variable_name | Value |
+---------------+-------+
| wait_timeout | 28800 |
+---------------+-------+

監視項目数は以下になります。
アイテム数 (有効/無効/取得不可) 　　1718 (1686 / 0 / 32)
1秒あたりの監視項目数(Zabbixサーバーの要求パフォーマンス) 15.63

過去の投稿の中で、監視アイテム数は1000くらいまでなら問題なく監視出来るという
回答がありましたが、監視アイテム数が多すぎるのでしょうか。
監視アイテム数を減らす以外の解決法やアドバイス等ありましたらよろしくお願いします。

また、下記ログもzabbix_server.logに出力されていたのですが、上記ログに関係するものなのでしょうか。

------------------------------------------------------------------------------
29072:20130107:185624.134 enabling SNMP checks on host [hogehoge03]: host became available
29073:20130107:185716.517 SNMP item [ifDescr] on host [hogehoge03] failed: first network error, wait for 15 seconds
29075:20130107:185731.403 resuming SNMP checks on host [hogehoge03]: connection restored
29073:20130107:185738.682 SNMP item [hrProcessorLoad] on host [hogehoge03] failed: first network error, wait for 15 seconds
29075:20130107:185759.477 SNMP item [hrProcessorLoad] on host [hogehoge03] failed: another network error, wait for 15 seconds
29075:20130107:185820.500 SNMP item [hrProcessorLoad] on host [hogehoge03] failed: another network error, wait for 15 seconds
29075:20130107:185835.517 resuming SNMP checks on host [hogehoge03]: connection restored
------------------------------------------------------------------------------