Steps to reproduce:

1. Upgrade rpm to 4.4.4
2. Start zabbix-server
3. Problem in log: Can't DROP 'c_dchecks_1'; check that column/key exists [alter table dchecks drop foreign key c_dchecks_1]

Result:
See log file:

current database version (mandatory/optional): 04000000/04000004
required mandatory version: 04040000
starting automatic database upgrade
completed 1% of database upgrade
completed 2% of database upgrade
completed 3% of database upgrade
completed 4% of database upgrade
completed 5% of database upgrade
completed 7% of database upgrade
completed 8% of database upgrade
completed 9% of database upgrade
completed 10% of database upgrade
completed 11% of database upgrade
completed 13% of database upgrade
completed 14% of database upgrade
completed 15% of database upgrade
completed 16% of database upgrade
completed 17% of database upgrade
completed 19% of database upgrade
completed 20% of database upgrade
completed 21% of database upgrade
[Z3005] query failed: [1091] Can't DROP 'c_dchecks_1'; check that column/key exists [alter table dchecks drop foreign key c_dchecks_1]

Tried in mysql:

ALTER TABLE `zabbix`.`dchecks` ADD CONSTRAINT `c_dchecks_1` FOREIGN KEY (`druleid`) REFERENCES `zabbix`.`drules` (`druleid`) ON DELETE CASCADE ON UPDATE RESTRICT;

Error occured:

ERROR 1452 (23000): Cannot add or update a child row: a foreign key constraint fails (`zabbix`.`#sql-b3e_c3fd`, CONSTRAINT `c_dchecks_1` FOREIGN KEY (`druleid`) REFERENCES `drules` (`druleid`) ON DELETE CASCADE ON UPDATE RESTRICT)