Dear Nils, thank you so much! Your answer was extremely helpful (or maybe I was too stupid, let's be honest). But just straight bumping "max_connections" up in my.cnf didn't help alot: now we are running with LA above 40.0 and the whole system is a bit slow.
 
And even much worse it is, we are now getting the following out of memory diagnostics (never seen those before):
 

[Mon Jun  4 17:05:22 2007] index.pl: DBD::mysql::st execute failed: Out of memory (Needed 1603040 bytes) at /home/otrs/bin/cgi-bin/../../Kernel/System/DB.pm line 440.
ERROR: OTRS-CGI-10 Perl: 5.8.8 OS: freebsd Time: Mon Jun  4 17:05:22 2007

 Message: Out of memory (Needed 1603040 bytes), SQL: 'SELECT DISTINCT st.id, st.tn, st.create_time_unix FROM  ticket st, queue sq  WHERE sq.id = st.queue_id AND st.ticket_state_id IN (1,4,6,7,8) AND st.queue_id IN (24,61) AND sq.group_id IN (44, 13)  AND st.tn LIKE '2007060110510' ORDER BY st.create_time_unix DESC LIMIT 5000'

 Traceback (69122):
   Module: Kernel::System::Ticket::TicketSearch (v1.194) Line: 2484
   Module: Kernel::Modules::AgentTicketSearch::Run (v1.10) Line: 288
   Module: Kernel::System::Web::InterfaceAgent::Run ( v1.8) Line: 651
   Module: /home/otrs/bin/cgi-bin/index.pl (v1.80) Line: 47

[Mon Jun  4 17:05:22 2007] index.pl: DBD::mysql::st fetchrow_array failed: fetch() without execute() at /home/otrs/bin/cgi-bin/../../Kernel/System/DB.pm line 477.
ERROR: OTRS-CGI-10 Perl: 5.8.8 OS: freebsd Time: Mon Jun  4 17:05:23 2007

 Message: Out of memory (Needed 1603040 bytes), SQL: 'SELECT DISTINCT st.id, st.tn, st.create_time_unix FROM  ticket st, queue sq  WHERE sq.id = st.queue_id AND st.ticket_state_id IN (1,4,6,7,8) AND st.queue_id IN (24,61) AND sq.group_id IN (44, 13)  AND st.tn LIKE '2007060110316' ORDER BY st.create_time_unix DESC LIMIT 5000'

 Traceback (69134):
   Module: Kernel::System::Ticket::TicketSearch (v1.194) Line: 2484
   Module: Kernel::Modules::AgentTicketSearch::Run (v1.10) Line: 288
   Module: Kernel::System::Web::InterfaceAgent::Run ( v1.8) Line: 651
   Module: /home/otrs/bin/cgi-bin/index.pl (v1.80) Line: 47

[Mon Jun  4 17:05:23 2007] index.pl: DBD::mysql::st fetchrow_array failed: fetch() without execute() at /home/otrs/bin/cgi-bin/../../Kernel/System/DB.pm line 477.
ERROR: OTRS-CGI-10 Perl: 5.8.8 OS: freebsd Time: Mon Jun  4 17:05:24 2007

 Message: Out of memory (Needed 1603040 bytes), SQL: 'SELECT DISTINCT st.id, st.tn, st.create_time_unix FROM  ticket st, queue sq  WHERE sq.id = st.queue_id AND st.ticket_state_id IN (1,4,6,7,8) AND st.queue_id IN (24,61) AND sq.group_id IN (44, 13)  AND st.tn LIKE '2007060110532' ORDER BY st.create_time_unix DESC LIMIT 5000'

 Traceback (69119):
   Module: Kernel::System::Ticket::TicketSearch (v1.194) Line: 2484
   Module: Kernel::Modules::AgentTicketSearch::Run (v1.10) Line: 288
   Module: Kernel::System::Web::InterfaceAgent::Run ( v1.8) Line: 651
   Module: /home/otrs/bin/cgi-bin/index.pl (v1.80) Line: 47

...
 
and ad infinitum. What is the problem with those negligible 1.6Mb of memory to allocate? I don't bother much, let it consume even 16Mb, we aren't short in total RAM so far. But where's THIS limit hidden? Somewhere in DBD::mysql maybe? Or there is some place where system limits are enforced at OTRS instance? But I can't recall myself imposing any limits on process memory... and where should I look for it? At least in which direction... it's Perl started from Apache - I was in a hope that mod_perl works, but top utility shows me a number of httpd processes and a number of separate perl processes, so I'm in a doubt now...
 
Thank you for your time and attention!
 
WBR,
Andrew