src/zabbix_server/trapper/active.c functions 'send_list_of_active_checks' and 'send_list_of_active_checks_json' supposed to include unsupported items it a list of active checks for a host after CONFIG_REFRESH_UNSUPPORTED interval expires. Relevant lines from SQL query: 'select ... from items where ... or (i.status=%d and i.lastclock+%d<=%d) ...'.
The problem is that .lastclock field of 'items' table is always NULL, i.e. proxy doesn't update .lastclock field when it receives item values from agents.
To check that I deleted proxy database and let proxy create a new empty one. After some period of time I performed query: 'select count from items where lastclock is not NULL' and got '0'.
Work-around for this issue is to manually set .lastclock field to some value in the past, i.e. 0. After that re-enabling of usupported items starts working again.