pgBouncer works great but occasionally becomes unavailable
The "Cannot assign requested address" part in the error message comes from the kernel TCP stack. When encountered intermittently, this typically means that the space of available sockets is exhausted because of too much sockets in wait state (TIME_WAIT, or less probably FIN_WAIT_1 or FIN_WAIT_2)

The range of socket ports can be output by cat /proc/sys/net/ipv4/ip_local_port_range. The default value on a stock Linux kernel is generally 32768 61000.

You may check the result of netstat -ton|grep WAIT on the client(s) and on the pgBouncer's host when the system is busy. The -o flag will show the timeout 
counters related to wait states.

If the total number of TCP sockets is close to 61000-32768=28232 then exhaustion of this range is likely your problem. Since a closed socket spends 60 seconds in TIME_WAIT state in normal condition, if  a client host connects more than 28232 times in one minute, new connections will fail with the mentioned error until ports are freed.

As a first workaround, the TCP ports range may be extended: 

 # echo "1025 65535" &gt;/proc/sys/net/ipv4/ip_local_port_range


If it's not satisfactory, check the tcp_tw_recycle and tcp_tw_reuse flags, also tunable through /proc/sys/net/ipv4 and sysctl.

They're defined as (from man tcp):


       tcp_tw_recycle (Boolean; default: disabled; since Linux 2.4)
              Enable  fast  recycling  of  TIME_WAIT  sockets.   Enabling this
              option is not recommended since this causes problems when  work‐
              ing with NAT (Network Address Translation).

       tcp_tw_reuse (Boolean; default: disabled; since Linux 2.4.19/2.6)
              Allow  to reuse TIME_WAIT sockets for new connections when it is
              safe from protocol viewpoint.  It should not be changed  without
              advice/request of technical experts.


Personally I had success with tcp_tw_recycle when faced with this problem with a MySQL client app, but don't take this as a recommendation, my understanding of TCP being superficial at best.